Road Less Traveled - 2434 Words

THE ROAD LESS TRAVELED DISCIPLINE #9;The Discipline section of M. Scott Pecks The Road Less Traveled first deals with lifes difficulties. He makes it clear that we all have problems and pain but we have to deal with it to get by and to make life less difficult. quot;Life is difficult... Once we truly know that life is difficult--once we truly understand and accept it--then life is no longer difficult. Because once it is accepted, the fact that life is difficult no longer matters.quot;(p.15) #9;The four main points of the Discipline section are delaying gratification, acceptance of responsibility, dedication to reality and balancing. These four points are referred to as tools to solve lifes problems. By using these†¦show more content†¦A genuinely loving person, he says, will take loving action toward a person whether he or she likes them or not. Genuine love implies commitment and the exercise of wisdom. quot;The common tendency to confuse love with the feeling of love allows people all manner of self-deception.quot;(p. 119) Love is the act of going the extra mile to make something work. He also calls it a form of courage. quot;If an act is not one of work or courage, then it is not an act of love. There are no exceptions.quot;(p. 120) Primarily the work is the attention one gives to the one he or she loves. This attention includes quot;true listening.quot; The courage comes into play because one should always fear the risk of loss, commitment, and confrontation. #9;Peck says that quot;love is separateness.quot; He confirms that it is important to nurture one anothers spiritual growth, but one major characteristic of genuine love is that the distinction between oneself and the other is always maintained and preserved. It is important that the two lovers maintain separate identities and individuality. He feels that it is the separateness of partners that enriches the union. quot;But let there be spaces in your togetherness,...Fill each others cup but drink not from one cup. Give one another of your bread but eat not from the same loaf...quot;(p.Show MoreRelatedTaking The Road Less Traveled1312 Words   |  6 PagesTaking the Road Less Traveled College is a time of learning, stress, and finding yourself. Every student should experiment and find what they love the most. College is a time to meet new people. Going to a school where you may not have a class with anyone you know can be nerve wracking. However, going into college while in a relationship is extremely difficult. I have been in a relationship with my current boyfriend for two years. However, starting college while in a relationship can lead to unneededRead MoreDecisions in The Road Less Traveled Essays657 Words   |  3 PagesDecisions in The Road Less Traveled The word decision is defined by Websters Dictionary as, the act of deciding, or judgement. People have to make decisions in their lives all the time. One of the largest decisions is what to do after high school. This decision is certainly going to take you in one direction of another. And the places where your decisions would take you can differ greatly. Similarly, The Road Not Taken by Robert Frost uses symbolism to demonstrate that everyone isRead MoreThe Road Not Taken By Robert Frost1286 Words   |  6 Pageshowever, no one can tell how each path will turn out, so saying the road less taken is the better choice has no evidence and is a useless statement. In his poem â€Å"The Road Not Taken,† Robert Frost gives thought about taking the road less traveled and how it has made a difference in his life, however each road is actually equal in taking and both can have positive and negative effects and there is technically no actual â€Å"road less traveled†. Frost d oesn’t say whether the difference is positive or not whichRead MoreAnalysis Of Frost s The Road Not Taken 1084 Words   |  5 Pagesfuture: whether it be the path that I follow in the end, or what I choose to believe. In â€Å"The Road Not Taken,† Frost helps to further illustrate these points. When he stumbles upon two separate paths, one that is worn and the other not quite so much, he is left to ponder which one he should follow. They both look relatively similar, but after a moment of contemplation, he decides to take the path less traveled: claiming that in the end it â€Å"has made all the difference.† I find myself drawn by thisRead MoreEssay about Themes in The Road Less Traveled699 Words   |  3 PagesThe Road Less Traveled M. Scott Peek starts off with life is difficult. Peck speaks of discipline and how it is the basic tool required to solve our problems. Life is a series of problems and what makes life difficult is the process of confronting and solving problems. These problems evoke in us frustration or grief or sadness, anguish or despair. yet it is in facing these problems that we gain wisdom, strength and courage. Any problem brings out a certain emotion; feelings and these feelingsRead MoreRoad Not Taken, Robert Frost942 Words   |  4 Pages101 Burstrem October 7, 2009 The Road Not Taken Life is full of choices and decisions that could ultimately change the outcome of our lives. In the poem, â€Å"The Road Not Taken† by Robert Frost, a traveler is destined to make that decision. This traveler man has to decide which road to take, one that is frequently traveled, and the one that is not. After contemplating which road to follow, he comes to the decision to take the road less traveled because he doesn’t want to follow in the footstepsRead MoreEssay on On The Road Not Taken1139 Words   |  5 PagesOn The Road Not Taken Most people believe that The Road Not Taken by Robert Frost was written to inspire people to be different, and to not follow the majority. However, the poem was actually written to gently tease one of Frosts good friends, and fellow poet, Edward Thomas. Frost and Thomas would take walks in the woods together, and Thomas would take Frost down one path and later regret not choosing a different path. This would lead one to believe that Frost is actually ridiculingRead MoreThe Road Not Taken By Robert Frost Essay1156 Words   |  5 PagesLee Frost was an American poet. His work was initially published in England before it was published in America. He is highly regarded for his realistic depictions of rural life and his command of American colloquial speech. Robert Frost’s poem â€Å"The Road Not Taken is a narrative poem on making decisions. A narrative poem is one that tells a story. It follows a similar structure as that for a short story or novel. There is a beginning, middle and an end, as well as the usual literary devices such asRead More Analyzing Themes in Robert Frosts The Road Not Taken Essay801 Words   |  4 PagesRobert Frosts The Road Not Taken This is a wonderful poem with many different themes and ideas. One of the biggest themes is not being afraid to take a chance. Some of the other themes include, not following the crowd, trying new things, and standing for something. This poem stated that the author took the one (road) less traveled by, and that has made all the difference so the author is telling the reader that we too should not be afraid to take another path. The Road Not Taken is aRead MoreAnalysis Of The Poem The Road Not Taken 808 Words   |  4 Pagessigh/Somewhere ages and ages hence:/Two roads diverged in a wood, and I--/I took the one less traveled by†¦Ã¢â‚¬  these are famous lines from a classic poem written by Robert Frost. The poem, â€Å"The Road Not Taken† was one of many poems written by Frost. This well-known poem is about the struggle of a traveler decision between two routes he could take. It has both literal and metaphorical meaning; the roads can also symbolize two paths of life to follow. The Road Not Taken†¯is told from a first-person point

Stress, Health, And Human Flourishing Essay - 800 Words

Chapter 11 – Stress, Health, and Human Flourishing The major focus of this chapter was stress and the effect it has on the body. Stress is the process by which we perceive and respond to certain events, called stressors, that we appraise as threatening or challenging. The concept of appraisal is the important part here. Stress can be affected through this psychological filter, either making the stressor feel threatening or challenging. The way we perceive it can have either positive or negative effects. Stress, when perceived negatively can lead to issues such as coronary heart disease or increased susceptibleness to colds (Myers, 2014). A Canadian scientist by the name of Hans Selye name the result of his research the general adaptation syndrome, or GAS for short. He described the process of stress as a 3-way process. There is phase one, alarm reaction, phase two, resistance, and phase three, exhaustion. Being unable to cope with a stressor and remaining in the last phase for too long can have negative health effects. Men and women both traditionally deal with stress in different ways. Men, and least more often than women, tend to socially withdraw, turn to alcohol, or become aggressive, while women more often respond by nurturing and bonding together (Myers, 2014). There are many ways to cope, or alleviate using emotional, cognitive, or behavioral methods, with stress. In this chapter, the three we discussed were catharsis, problem-focused, and emotion-focused.Show MoreRelatedThe National League Of Nursing Competencies1406 Words   |  6 PagesHuman Flourishing Human flourishing, one of the National League of Nursing competencies, refers to the overall state of well-being of an individual within multiple contexts. This competency celebrates diversity, freedom, happiness, and holistic well-being of individuals within their families, communities, and society (Nursing Framework and Program Outcomes, n.d.). The concept of human flourishing embodies the elements of contrast and conflict in life, connection with the surrounding world,Read MoreThe Effects Of Physical Exercise On The Brain Essay1439 Words   |  6 PagesThe human brain is constantly changing where many new neurons are formed while others neurons die and new synapses are created while other synapses are removed (Spalding et al., 2013). Some dendrites will withdraw while other dendrites continue branching (Killgore et al., 2013). The processes driving the reshaping of the brain are neuroplasticity and neurogenesis. Neuroplasticity is the brain’s lifelong ability to rewi re neural connections to compensate for diseases and injuries or in response toRead MoreThe Catholic Church Should Accept That Gay Marriage1526 Words   |  7 Pagesthe spouses and the procreation and education of offspring. So, the main point of marriage is for a joining of sorts of two people so they can procreate or have children. These are all goods in the eyes of the Church. A good is what lead to human flourishing or journeying back to God. Examples of these goods are life itself, communion with others, marriage, sexuality, and children. Heterosexual marriage complies with these goods. Gay marriage complies with these goods besides one. The one beingRead MoreA Portrait Of A Killer1042 Words   |  5 PagesPortrait of a Killer, examines the types of stress that living beings can endure, and how it can thus affect the rest of their bodies. Severe chronic stress can lead even lead to the destruction of brain cells. Dr. Robert Sapolsky is a neurobiologist of Stanford Univ ersity who has been researching stress for over thirty years. In order to study stress and its implications upon nonhumans, he went to Africa to study baboons. This species has only three hours of stress caused by eating, and the rest of theirRead MoreHuman Resource Planning595 Words   |  3 PagesHuman Resource Planning The function that I will explore in depth is Marks and Spencer human resource planning primarily concerned with the organisation possessing sufficient numbers of employees and of the right standard. The four main purposes of the human resource planning function are:  · Marks and Spencer establish clear links between organisational objectives and human resource plans so that successful co-ordination of the two can be set out.  · To giveRead MoreThe Effects Of Obesity On An Individual s Health And Well Being954 Words   |  4 Pagesmay affect the health and illness experiences of its members. Include information about specific services and health promotional activities that may be available for this group. You should also examine issues of discrimination and bias in relation to this group, how this might have changed over time, and how this might influence group members’ use of services. Adult obesity stigmatisation Introduction This essay will consider the holistic impact of obesity on an individual s health and well-beingRead MoreIvb Essay749 Words   |  3 PagesPGD to test for serious inherited genetic disorders. Funding includes costs of the IVF treatment which accompany PGD. Only some may be able to afford PGD therefore public funding is important to ensure fair and equitable opportunity.4 PGD reduces health care costs. Treatment of some genetic diseases can cost millions over the lifetime for a single individual. Avoiding these births would save money. Ethical: Many believe termination after prenatal diagnosis is unacceptable. There are many beliefsRead MoreEthics Of The Good Life For A Human Being1398 Words   |  6 Pagesfor a human being. Through living with the mean state and with moral virtue, the disposition to behave in the right manner and as a mean between extremes of deficiency and excess, Aristotle explains how one can reach the end purpose of life and achieve eudaimonia, human flourishing. Aristotle’s fundamental claims surrounding moral excellence and habituation allow to one enact the necessary process of moderating thinking and feeling to become a morally excellent person. In order to reach human thrivingRead MoreAssess The Organization s Programs And Services Essay1706 Words   |  7 Pagesthe State of Arizona. The Area Agency on Aging Region One’s programs include a 24 hour Senior Help Line, Elder Resource Guide, Adult Day Health Care, Adult Protective Services Service Coordination (APS), AgeWORKS, Benefits Assistance Medicare Program, Care Transitions Healing@Home, Congregate meals, Doves Program, Eldervention, Family Caregiver Support, Health Promotion, HIV Care Directions, Home-Delivered Meals, Legal Assistance, Long-term Ombudsman, Los Ancianos Seniors Serving Seniors, MaricopaRead MoreWhat Is Education Important?2263 Words   |  10 Pagesexistence, the use and limits of knowledge and the principles that govern and influence moral judgement (Dictionary, 2016). The word philosophy is a geek word with the meaning of love of wisdom , philosophers research meaning of concepts to clarify human nature and knowledge (Bates.J et al, 2009). Philosophers that look into education ask many questions to get the definition, aims and purposes of what education is (Bates et al, 2009). Besides knowing the definitions of education, philosophers would

Music Videos Debate Essay Example For Students

Music Videos Debate Essay Music is prominent in adolescent lives: teenagers spend between 4 and 5 hours a day listening to music and watching music videos 1 and name music listening as their preferred non-school activity. 2 Therefore, it is not surprising that government officials, researchers and parents alike are concerned about the impact of music on teenagers. Disturbed by the amount of violence portrayed in modern music, adults worry that these messages are contributing to the rise in violence among kids. Forty-eight percent (48%) of Americans say that violence in popular music should be more heavily regulated 3 and 59% would like to restrict violence in music. 4Music LyricsForty-seven percent (47%) of mothers with children in public schools believe that violent messages in rap music contribute â€Å"a great deal† to school violence, 5 and 66% of 13- to 17-year-olds believe violence in music is partly responsible for violent crimes like the 1999 Columbine High School shootings. 6 However, no studi es have documented a cause-and-effect relationship between violent or sexually explicit lyrics and adverse behavioral effects. 7 Studies show that the preference for heavy metal music may be a significant indicator for alienation, substance abuse, psychiatric disorders, suicide risks, sex-role stereotyping, or risk-taking behaviors during adolescence, 8 but music is not the cause of these behaviors. It is hypothesized that teenagers already struggling with those issues may be attracted to heavy metal music, because the lyrics express their own troubled feelings. Nonetheless, music may contribute to the atmosphere of violence that some argue is generated by popular media. Critics claim that music negatively affects teenagers by repeatedly exposing them to themes such as Satanism, substance abuse, murder, suicide and sexual violence, which may be heavily reinforced and normalized by the frequency of their portrayal. 9 Heavy metal and rap music are especially criticized for lyrics that many believe glorify violence. Music lyrics have also become increasingly explicit in the past two decades. Songs commonly make graphic references to sex, drugs and violence, whereas such sensitive topics were cleverly veiled in the past. 10In particular, â€Å"gangsta rap† is distinguished by lyrics that often involve references to street gangs, gunplay, sex, drug use and violence, and has been accused of extolling violent behavior. Studies have found that exposure to rap music â€Å"tends to lead to a higher degree of acceptance of the use of violence.à ¢â‚¬  11 In addition, several major rap artists have been charged with violent crimes in real life, 12 and many worry that their actions seemingly condone the violent messages in their music. Their celebrity status also serves to glamorize their violent behavior. Music VideosMusic Television (MTV) redefined music for future generations by creating music videos, and the unique fusion between rock music and visual images continues to be a hit. A 1996 study revealed that boys and girls ages 12 to 19 watch MTV for an average of 6.6 and 6.2 hours each week, respectively. 13 But despite music videos’ popularity among adolescents, many adults criticize the medium as studies show that music videos often contain violence, sexism, suicide and substance abuse. 14 A 1998-1999 study revealed that music videos were more violent than feature films and television, averaging four violent scenes each, 15 and a 1997 study reported that 22.4% of MTV videos contained overt violence and 25% depicted weapon carrying. 16The American Academy of Pediatrics reported that portrayals of violence in popular music videos could distort adolescents’ expectations about conflict resolution, race and male-female relationships. 17 In a 1998 study of 518 music video s from the four most popular music video networks, almost 15% contained interpersonal violence, averaging 6 violent acts per violence-containing video. 18 Males and females were equally portrayed as victims of violence, but men were three times as likely to be the aggressors and white females were most frequently the victims. 19 African Americans were also overrepresented as both aggressors and victims and were 28 times more likely to be portrayed as victims of violence than aggressors. 20How much music videos affect teenagers depends on the individual, but researchers argue that when music lyrics are illustrated in music videos, the lyrics’ potential impact is magnified by the accompanying video images. 21 Ambiguous song lyrics become undeniably concrete onscreen, reinforcing messages listeners may have missed. Several studies indicate that music videos may desensitize adolescents by frequently exposing them to violence. 22 Watching videos may also induce violent and aggress ive feelings, potentially cultivating attitudes that may lead to certain types of violent behavior. One study of 400 male and female students showed that the more violent music videos were, the more angry, fearful and aggressive viewers felt. 23 Another study reported that eliminating access to MTV decreased the number of violent acts among teenagers and young adults in a locked treatment facility. 24Some researchers raise concerns regarding depictions of women as sexual objects in music videos, where inappropriate behavior, such as unwanted sexual advances and general disrespect towards women, is repeatedly portrayed as normal. Sut Jhally, a communications professor at the University of Massachusetts-Amherst, created a video entitled â€Å"Dreamworks: Desire/Sex/Power in Rock Videos,† which effectively shows how music videos dehumanize women, reducing them to body parts readily available for the sexual satisfaction of men. Although outright violence towards women is rarely s hown, it is implied through stage props like whips and chains and is reinforced by the women’s permissive attitudes. Jhally stresses that music videos do not cause violence, but may encourage unrealistic expectations regarding women, leading to certain types of sexist attitudes and behaviors. â€Å"The more TV you watch, the more you think the world is like TV,† Jhally explains. â€Å"You tend to act on the stories you have access to.† 25

Security Organs in the US

Defense Support of Civil Authorities and its importance Defense Support of Civil Authorities (DSCA) denotes the process through which the US military can be deployed to undertake tasks that are meant for the civil authorities (Tussing McCreight, 2014). Conventionally, the military is charged with the responsibility of defending the US territories against intrusion by foreigners.Advertising We will write a custom research paper sample on Security Organs in the US specifically for you for only $16.05 $11/page Learn More However, in the contemporary times, the role of the US military has changed greatly due to increased terrorist activities. The US military now works with the civil authorities in mitigating domestic crimes and in other rescue missions during disasters. The DSCA is headed by The Directorate of Military Support for Domestic Operations (DOMS) and each state has a single DOMS. The DOMS is responsible for discharging military equipments and per sonnel to areas of disasters when called to do so by the office of emergency management. The basic roles, functions, missions, and capabilities of the National Guard The National Guard is a special military reserve unit established at around 1636 (Buchalter, 2007). It is composed of citizen-soldiers and they are mandated to serve in the army while preserving their civilian lives. The National Guard is made up of two branches, viz. the Air National Guard and the Army National Guard. The National Guard’s personnel are skilled men and women who provide technical support to the military in times of special needs. The mission of the National Guard is primarily to offer support to the military in times of active warfare. Initially, such support was only afforded in active warfare involving the US and a foreign country. However, the mission is changing with the changing nature of attacks within the US territories. Terrorist attacks have increased tremendously within the US, thus fac ilitating the deployment of the National Guard in the homeland security. In pursuance of this mission, the National Guard was employed during the Second World War to contain the Soviet Union.Advertising Looking for research paper on government? Let's see if we can help you! Get your first paper with 15% OFF Learn More The National Guard’s main responsibility is to provide professional support to the active soldiers in times of war (Buchalter, 2007). With the introduction of the â€Å"Total Force Concept† in the 1970s, the role of the National Guard has changed greatly (Tussing McCreight, 2014). The concept was launched by Melvin Laird, the then secretary of defense. The move followed concerns from the public over excessive expenditure on the Vietnam War. The total force concept requires cooperation amongst all elements of the forces. In other words, the concept increased the National Guard’s involvement in the US security. The National Guard also assists in the homeland security (Buchalter, 2007). Given that unit personnel are deployed in almost every community in the US, they act as intermediaries between the federal government and the local communities. They have the skills and authority needed to respond to terrorist attacks in the homeland. There are about 3,000 armories located across the US, which is a clear indication that they also assist the federal government in maintaining homeland security on top of providing emergency services to the military in times of active participation. In addition to providing assistance to the army and maintaining the homeland security, the National Guard offers training to local first responders (Buchalter, 2007). The training centers on emergency response in case of chemical, biological, radiological, or nuclear (CBRN) events (D’Agostino, 2010). The training benefits the rest of the military as well as local law enforcers. Presently, the National Guard has roughly 3,000 personne l trained to operate in hazardous environment such as chemically contaminated environments. In addition to providing military support in times of war between the US and a foreign power, the National Guard also participates in domestic issues. The National Guard is subdivided into units deployed in all the 50 states making up the US (Buchalter, 2007).Advertising We will write a custom research paper sample on Security Organs in the US specifically for you for only $16.05 $11/page Learn More The units operate under the governors of their respective states and at times, they may be ordered to participate in the provision of emergency services in times of disasters in their respective states. The unit is called upon to respond to natural calamities such as hurricanes, floods, and earthquakes. However, the state employing the services of the National Guard in such incidences should pay some fee to the federal government to obtain consent (D’Agostino, 2010). The concept of Defense Support of Civil Authorities The local law enforcement agencies regularly require the support of the military in critical situations (Tussing McCreight, 2014). The deployment of the military under the DSCA is the last resort after all other means have failed. The Federal Emergency Management Agency (FEMA) is authorized to deploy federal resources to any state in times of disasters upon request by a state. FEMA can command any local federal forces to join in mitigating a disaster in any state, but it can only request the military’s support when all other agencies have failed to contain the situation (Buchalter, 2007). Every federal agency is at liberty to appeal for military help. However, the agency seeking for the assistance should specify on the nature and extent of the assistance needed using a memorandum. Military aid is synchronized with the local authorities in the area where such assistance is needed. This aspect ensures that the support is maximized. Decisions regarding withdrawal or continuance of the support are made by the DoD officials, local government, and federal agencies (Tussing McCreight, 2014). A new memo must be prepared if changes are to be made to the original request. There are plentiful other decrees, principles and laws that govern the armed forces’ function in carrying out operations aimed at supporting the local authorities (D’Agostino, 2010). The laws include the Insurrection Act, Homeland Security Act, and the Homeland Security Presidential Directive – 5 (Buchalter, 2007).Advertising Looking for research paper on government? Let's see if we can help you! Get your first paper with 15% OFF Learn More The aforementioned rules apply to the concept of DSCA and determine military response to calls for assistance. When local law enforcers deploy the assistance of DSCA, the forces so employed immediately become answerable to the operational control of U.S. Northern Command (USNORTHCOM). Explain DOD’s roles and responsibilities in homeland defense The Department of Defense (DoD) is a department within the federal government charged with the responsibility of managing and overseeing all the activities of the federal security organs (Buchalter, 2007). The department is the largest employer worldwide and it has over 3 million employees. Its employees are not only military men, but also civilians who execute other special functions. The department oversees all the security operations in the US under the watch of the Secretary of Defense. The secretary of defense is answerable to the president of the US. There are three departments within the DoD, viz. the U.S. Department of the Army , the U.S. Department of the Navy, and the U.S. Department of the Air Force (Buchalter, 2007). The intelligence departments are also under this department. The department’s major functions are outlined below. DoD chief function is to coordinate the operations of the US security organs (D’Agostino, 2010). The department allocates resources to various security organs depending on the needs of the security organ in question. The department organizes and conducts recruitment for military personnel. In addition, DoD retains the resources for the military and only releases them when needed. DoD is responsible for the procurement of military equipments necessary for the working of the military. The department is also charged with the responsibility of ensuring that the military remains equipped and ready to counter attacks that may arise. The department, through the various intelligence departments that operate under it, is responsible for providing intelligence reports to th e president regarding the security of the nation (Tussing McCreight, 2014). The intelligence community is charged with the responsibility of providing warnings to security agents of security threats prior to their occurrence. The IC is composed of highly trained crime detectives with the ability to detect crime before it is accomplished. It is composed of both the military and civilians. The security officers in charge of providing global security rely greatly on the IC’s report to combat terrorism and protect the citizens around the world. All the intelligence departments are under the DoD and intelligence reports are submitted to the DoD, which in turn presents it to the president (Buchalter, 2007). The intelligence report is important to a nation’s security since it warns the country of an attack before it is accomplished. The DoD’s objectives in homeland defense The primary objective of the DoD is to secure the US territories from foreign attacks (D’ Agostino, 2010). The department has well skilled and equipped personnel who ensure that the American territories remain secure. With the increasing terrorist attacks, the department aims at achieving full protection of its boarders and counter crime. In a bid to accomplish this mission, the department recruits qualified personnel and affords the necessary training to equip them with the necessary skills to counter attacks. In addition, the department has highly experienced intelligence personnel with the ability to detect crime before it is accomplished. This objective extends to cover containing major threats to the world’s security. The second objective that the DoD is obliged to meet is homeland security (Gates, 2009). The department has highly trained staff and it avails assistance to the local law enforcers as and when needed. Its objective is to train military personnel to handle different types of crimes including nuclear attacks. How the US employs all elements of nat ional power in homeland defense The military’s primary function is to protect the US territories against external attacks. However, this role has extended to the provision of emergency services and support to the civil authorities (Gaston, 2011). The military only comes to support the civil authorities. Crises are managed at the lowest level by the civil authorities, but when the nature of the crisis turns critical and it can no longer be managed by the local authorities, the military is deployed to assist. Military support is requested by the agency in need of the support and it is required to pay the cost incurred by the army. The requesting agency is required to file a memo to the DOMS containing the nature of support needed and the estimated cost of the operation. The US military collaborates with the civil authorities in times of disasters and in countering riots and demonstrations by the public in major towns in the US. However, the military is employed in situations wh ere the local law enforcement agencies cannot manage due to lack of skills or equipment (Tussing McCreight, 2014). Defense Support of Civil Authorities is an important aspect of security in the US since it ensures that the country is secure at all times. The military at times share training facilities and equipments with the local civilians increasing the ability of the local law enforcers to counter attacks. References Buchalter, R. (2007). Military Support to Civil Authorities: The Role of the Department f Defense in Support of Homeland Defense. Retrieved from http://www.loc.gov/rr/frd/pdf-files/CNGR_Milit-Support-Civil-Authorities.pdf D’Agostino, M. (2010). Homeland defense: DOD can enhance efforts to identify capabilities to support civil authorities during disasters. Collingdale, PA: DIANE Publishing. Gaston, R. (2011). Standardizing readiness and response in defense support of civil authorities. Retrieved from https://apps.dtic.mil/dtic/tr/fulltext/u2/a553166.pdf Gates , M. (2009). National defense strategy. Collingdale, PA: DIANE Publishing. Tussing, B., McCreight, R. (2014). Introduction to Homeland Defense and Defense Support of Civil Authorities (DSCA): The U.S. Military’s Role to Support and Defend. Boca Raton, FL: CRC Press. This research paper on Security Organs in the US was written and submitted by user Damarion U. to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.

School Vouchers essays

School Vouchers essays Education School Vouchers There has been a lot of debate recently over the use of school vouchers. Voucher programs offer students attending both public and private schools tuition vouchers. It gives taxpayers the freedom to pick where their tax dollars go. In theory, good schools will thrive with money and bad schools will lose students and close its doors. Most people feel that taking taxpayer money from public schools and using this money as vouchers for private schools is a violation of the constitution. Most private schools in America right now are run by religious organizations. There has been a lot of controversy over this issue mainly because of the importance of an education in a modern society. School choice initiatives are based on the premise that allowing parents to choose what schools their children attend is not only the right thing to do, but is also an important way for improving education. Instead of a one-size-fits-all model, School choice programs offer parents various options from which to pick the educational settings they believe will work best for their child. However, there is Supporters of school vouchers claim that it levels the educational playing field for lower income families who would have the option to send their kids away from an ineffective poorly funded public schools. Some lower class families feel that their kids would have a better chance with a tuition voucher to go to a private school where more money is spent on education. Many feel that vouchers would undermine public schools, by taking away public money for smaller class sizes, teacher training and innovative curriculum. Also, many feel that vouchers would erode the support for public education. In Milwaukee, voucher schools say they do not give special services to students with disabilities. Most of the voucher schools refused to sign a letter that they will ...

Lines of Longitude in Geography

Lines of Longitude in Geography Longitude is the angular distance of any point on Earth measured east or west of a point on Earths surface. Where Is Zero Degrees Longitude? Unlike latitude, there is no easy point of reference such as the equator to be designated as zero degrees in the longitude system. To avoid confusion, the worlds nations have agreed that the Prime Meridian, which passes through the Royal Observatory in Greenwich, England, will serve as that reference point and be designated as zero degrees. Because of this designation, longitude is measured in degrees west or east of the Prime Meridian. For example, 30Â °E, the line passing through eastern Africa, is an angular distance of 30Â ° east of the Prime Meridian. 30Â °W, which is in the middle of the Atlantic Ocean, is an angular distance of 30Â ° west of the Prime Meridian. There are 180 degrees east of the Prime Meridian and coordinates are sometimes given without the designation of E or east. When this is used, a positive value represents coordinates east of the Prime Meridian. There are also 180 degrees west of the Prime Meridian and when W or west is omitted in a coordinate a negative value such as -30Â ° represents coordinates west of the Prime Meridian. The 180Â ° line is neither east nor west and approximates the International Date Line. On a map (diagram), lines of longitude are the vertical lines running from the North Pole to the South Pole and are perpendicular to lines of latitude. Every line of longitude also crosses the equator. Because longitude lines are not parallel, they are known as meridians. Like parallels, meridians name the specific line and indicate the distance east or west of a 0Â ° line. Meridians converge at the poles and are farthest apart at the equator (about 69 miles (111 km) apart). Development and History of Longitude For centuries, mariners and explorers worked to determine their longitude in an effort to make navigation easier. Latitude was determined easily by observing the inclination of the sun or the position of known stars in the sky and calculating the angular distance from the horizon to them. Longitude could not be determined in this way because Earths rotation constantly changes the position of stars and the sun. The first person to offer a method for measuring longitude was the explorer Amerigo Vespucci. In the late 1400s, he began measuring and comparing the positions of the moon and Mars with their predicted positions over several nights at the same time (diagram). In his measurements, Vespucci calculated the angle between his location, the moon, and Mars. By doing this, Vespucci got a rough estimate of longitude. This method did not become widely used however because it relied on a specific astronomical event. Observers also needed to know the specific time and measure the moon and Mars positions on a stable viewing platform- both of which were difficult to do at sea. In the early 1600s, a new idea to measure longitude was developed when Galileo determined that it could be measured with two clocks. He said that any point on Earth took 24 hours to travel the full 360Â ° rotation of Earth. He found that if you divide 360Â ° by 24 hours, you find that a point on Earth travels 15Â ° of longitude every hour. Therefore, with an accurate clock at sea, a comparison of two clocks would determine longitude. One clock would be at the home port and the other on the ship. The clock on the ship would need to be reset to local noon each day. The time difference would then indicate the longitudinal difference traveled as one hour represented a 15Â ° change in longitude. Shortly thereafter, there were several attempts to make a clock that could accurately tell time on the unstable deck of a ship. In 1728, clockmaker John Harrison began working on the problem and in 1760, he produced the first marine chronometer called Number 4. In 1761, the chronometer was tested and determined to be accurate, officially making it possible to measure longitude on land and at sea. Measuring Longitude Today Today, longitude is more accurately measured with atomic clocks and satellites. The Earth is still divided equally into 360Â ° of longitude with 180Â ° being east of the Prime Meridian and 180Â ° west. Longitudinal coordinates are divided into degrees, minutes and seconds with 60 minutes making up a degree and 60 seconds comprising a minute. For example, Beijing, Chinas longitude is 116Â °2330E. The 116Â ° indicates that it lies near the 116th meridian while the minutes and seconds indicate just how close it is to that line. The E indicates that it is that distance east of the Prime Meridian. Although less common, longitude can also be written in decimal degrees. Beijings location in this format is 116.391Â °. In addition to the Prime Meridian, which is the 0Â ° mark in todays longitudinal system, the International Date Line is also an important marker. It is the 180Â ° meridian on the opposite side of the Earth and is where the eastern and western hemispheres meet. It also marks the place where each day officially begins. At the International Date Line, the west side of the line is always one day ahead of the east side, no matter what time of day it is when the line is crossed. This is because the Earth rotates east on its axis. Longitude and Latitude Lines of longitude or meridians are the vertical lines running from the South Pole to the North Pole. Lines of latitude or parallels are the horizontal lines running from the west to the east. The two cross each other at perpendicular angles and when combined as a set of coordinates they are extremely accurate in locating places on the globe. They are so accurate that they can locate cities and even buildings to within inches. For example, the Taj Mahal, located in Agra, India, has a coordinate set of 27Â °1029N, 78Â °232E. To view the longitude and latitude of other places, visit the collection of Locate Places Worldwide resources on this site.

Rolls royce anual report Coursework Example | Topics and Well Written Essays - 1000 words

Rolls royce anual report - Coursework Example The external auditor of the company has given an opinion according to which the group financial statements of the company present a true and fair view for the financial year ending December 31, 2012. The auditor reports states that the group financial statements are adequately prepared in accordance with the International Financial Reporting Standard (IFRS) and Companies Act 2006. It is also mentioned in the audit report that the financial statements of the company have been prepared in accordance with the Generally Accepted Accounting Principle (GAAP) as adopted by European Union. The audit report forms an integral part of the financial statements of a company, especially a public listed company. The primary purpose of the audit report is to bring into the knowledge of the users of the financial statements whether these financial statements are prepared in accordance with the applicable financial reporting framework. [Readyratios.com (2011)] Users of the financial statement usually do not have the time to thoroughly analyze the authenticity of the financial statements. They take reliance of from the audit report that whether the financial statements are giving a true and fair view or not. ... 69% 3% Current ratio 1.33 1.2 1.70 Inventory turnover period 109 days 112 days 50 days Payables’ turnover period 247 days 262 days 20 days Gearing ratio 1.967 2.634 4% P/E ratio 7.1 16.43 9.0 x Answer to Question No. 4 2012 2011 Variation % variation Change in million ? Sales 12,161 11,124 1,037 9.32% Rise Operating Profit 1,373 1,186 187 15.77% Rise Share Price (pence) 874 755 118 15.66% Rise Answer to Question No. 5 During the current financial year, the return on equity (ROE) has considerably increased during the current financial year. The return on equity is calculated by dividing the net profit attributable to shareholders by the shareholders equity. [Investopedia, 2012] The ratio is quite essential from the investor’s point of view as it represents how well a company is earning on its shareholder equity, which mainly comprises of issued capital and retained earnings. The ROE of the company has increased during the financial year 2011 which is due to the fact that the net profit of Rolls Royce has increase by a staggering 170% as it increased from 848 million to 2,295 million. The main reason behind this increase in the net profit is one unusual item of 669 million which is due to the disposal of a segment of the business during the current financial year. It would also be worth mentioning that the sales and operating profit of the company has increased by 9.32% and 15.77% during the current financial year. These escalations in figures have further accentuated the return on equity during the current year. The ratio is better than the industry average which is a sign for positive financial outlook. The gross profit has increased marginally during the current financial year. The reason behind the marginal increase in the gross profit margin is the fact that

Customer relationship Case Study Example | Topics and Well Written Essays - 2500 words

Customer relationship - Case Study Example Abrupt usage of such principles had ultimately made customer the king in the global economy of today. As almost all of the market follows the perfect competition, so the decision precisely depends upon the buyer to choose the services of which company they want to purchase. As the customer has been the most important aspect that has to be cared by the companies, the concept of customer relationship becomes immensely important. The present day companies try and develop stable and trust worthy relationship with the esteemed customers so that the relationship is maintained and retained. The modern theory suggests that it is very difficult to have a new customer in favour of a company due to increased competition. Therefore, the onus lies on the companies to develop a mutually benefitting relationship so that the customers as well as the organisations benefit and the existing customers are retained apart from attracting newer customers. Established in 2001, the Lebara Group had objective to offer exciting and innovating telecom solutions to the families and the friends of the customer. The group falls under the greater preview of Lebara Foundation, which is a charitable trust with the aim to assist the deprived children all across the globe. The vision and the mission statement of the organisation says that the charitable trust aims to provide good life to the deprived children in terms of basic necessities like that of food, shelter, treatment (for both mental as well as physical illness), education and various skill sets required to get settled in life. Lebara Mobile was first launched in 2004 in the land of Netherlands as the low cost international mobile service. The group offers prepaid mobile SIM cards in at least eight European nations which include the advanced nations like Netherlands, Australia, Denmark, Norway, Spain, Switzerland, United Kingdom and Sweden. The various unique selling propositions of the products of the company include: Very low rates Instant connections High quality networks Multilingual customer services Reliable service No access codes No hidden charges No lost minutes (Lebara, n.d.) The company claims to have 24 X 7 reliability monitoring. Also it has a dedicated routing and switching teams to retain the high quality. But the most important factor of the Lebara Telecom Group is that of its low cost. And the factor is guaranteed by its team of global carrier. The international calls of the mobile group are routed by the London Network Operations Centre. Customer Relationship of Lebara The customer relationship of Lebara Group is quite commendable. As the group has presence in more than 8 countries, also the policies adopted by the group are aimed to retain the existing customers along with attracting new clients. The group has declared objective of providing the customers with value for money along with ensuring all of its connections with the best possible quality. As the objective of the group is to connect the customers with their friends and relatives all across the globe, so it takes special measure to ensure that the customers get the convenience of direct-dial international mob

Mother Teresa Essay Example for Free

Mother Teresa Essay Mother Teresa was determined to help as many poor and homeless people as possible. She was always thinking of the many people in need. Everyone said about her â€Å"either move out of her way or help the poor.† They said that because she was always helping the poor and she wouldn’t let anyone or anything get in her way. She never cared about herself getting sick, all she cared about was the people in need. The reason why I want to be like Mother Teresa is because I want to make a difference in people’s lives just like she did. Also, I want to be like her because she was always thinking of others. Mother Teresa was very ambitious because she never rested until all of her patients were comforted because she saw the face of Jesus in all of them. God talked to Mother Teresa a lot. Once when she was on a train she heard God say to her, â€Å"get off the train and help the people in need.† So she did. She would always obey God’s orders. Whenever a person came up to her to ask for help she would help them with anything like if they needed food, care, or help with anything she was always there. That is another reason why I want to be like Mother Teresa. Mother Teresa is very worthy of imitation. Every day of Mother Teresa’s life since she became a nun, she was working with people. Mother Teresa served the poorest of the poor for over 45 years. Thanks to Mother Teresa, now there are many places for the homeless, poor, the unwanted, and lots more. Pope John Paul II said â€Å" Mother Teresa marked the history of our century with courage. She served all human beings by promoting their dignity and respect, and made those who had been defeated by life feel the tenderness of God.†

The Anchoress of England: Julian of Norwichs Portrait of Christ as Mot

The Anchoress of England: Julian of Norwich's Portrait of Christ as Mother      Ã‚  Ã‚  Ã‚  Ã‚   When speaking of medieval literature, Chaucer, Gower and Langland are quite often the most noted. However, recent studies have provided modern scholars with a wide variety of medieval women writers from all over Europe and a few in England. The most widely anthologized English female writer is Julian of Norwich. Julian was an anchoress, and as Marcelle Thiebaux notes, "The anchorite movement was widespread in England from the eleventh to the fifteenth centuries. Both men and women chose this extreme form of asceticism, which was favored and encouraged by the crown, the church, and the laity. Anchorholds were small, narrow cells attached to churches or friaries" (442). 1[1] The process of becoming an anchoress was difficult and complicated, but suffice it to say that after the process was completed "the anchoress was sealed up, never to re-emerge into the world. Penance, meditation, reading, and in some cases writing were the anchorite's sole activities" (Thiebaux 442).   This was the case for Julian of Norwich. She was "well read in Scripture, dwelling especially on the Psalms, the gospels, and the epistles of Paul and John, ...and was the first English woman to write a book" (Thiebaux 443-44). Her Book of Showings to the Anchoress Julian of Norwich 2[2]   possesses literary and religious value, and the work lends itself quite naturally to a feminist reading. In her clear, lucid, prose style, combined with the images of the medieval mystic, Julian establishes herself as an independent, female religious authority and she gives a staunch affirmation of the divinity of God with this unique view point: the motherhood of God.      Ã‚  Ã‚  Ã‚   In her fi... ...7. All biblical references come from the Geneva Bible (which is based on the Jerome Bible) but were checked and crossed referenced with the Jerome Bible with help of Professor Behunin as the Jerome Bible is in Latin. 7[7] It is interesting to note that there might be a biblical correlation to the hazelnut. The name Hazel appears in the Bible, and in Jewish the name Hazel is a feminine name and means "one who sees God." ( Harrison, R.K. Biblical Hebrew England: Hodder & Stoughton, 1986.) 8[8] Sir Gawain and the Green Knight. Trans. Marie Borroff. Norton Anthology of British Literature Vol. 1, New York: WW Norton, 1993. 9[9] The "five fives" as they are known in medieval literature and religion can be found in Sir Gawain and the Green Knight. Trans. Marie Borroff. Norton Anthology of British Literature Vol. 1, New York: WW Norton, 1993, lines 640-654.   

An Analysis of Robert Francis’ Poem The Hound Essay

In Robert Francis’ poem â€Å"The Hound,† the writer creates a sense of fear by comparing how mysterious and unpredictable dogs are to life using an extended metaphor to show life as uncertain and one has to wait to see what it brings at them. In lines 1-5, the writer states: â€Å"Life the hound/Equivocal/Comes at a bound/Either to rend me/Or to befriend me.† The speaker compares the habits of a hound to life to show even though they are not alike, they are similar in the way of not knowing the next thing that can happen. They are both questionable and suspicious because no one knows what will happen next and there is a possibility of it tearing one apart. Additionally, it can be a friend to one and everything will go well. This enforces how uncertain life is towards human beings. Meanwhile, the speaker continues in lines 6-11 by saying: â€Å"I cannot tell/ The hound’s intent/ Till he has sprung/ At my bare hand/ With teeth or tongue.† There is a sense of tension that is created in these lines by the use of imagery in order to show how no one is sure of what will follow. There is a possibility that life won’t be very friendly and will come at one â€Å"with teeth or tongue.† This can seem like a negative thing because it could come and bite you or that phrase could mean it is coming with happiness and joy thus promising good things to come. Finally, the speaker says in the last two lines â€Å"Meanwhile I stand/And wait the event.† This suggests the speaker is passive and waiting for something to happen. This is because one doesn’t know what will happen thus will not actively participate. In life, one might not always participate because life is uncertain and it can either be a friend or destroy the person.

College Physics 9e

1 Introduction ANSWERS TO MULTIPLE CHOICE QUESTIONS 1. Using a calculator to multiply the length by the width gives a raw answer of 6783 m 2 , but this answer must be rounded to contain the same number of signi? cant ? gures as the least accurate factor in the product. The least accurate factor is the length, which contains either 2 or 3 signi? cant ? gures, depending on whether the trailing zero is signi? cant or is being used only to locate the decimal point. Assuming the length contains 3 signi? cant ? gures, answer (c) correctly expresses the area as 6. 78 ? 10 3 m 2 .However, if the length contains only 2 signi? cant ? gures, answer (d) gives the correct result as 6. 8 ? 10 3 m 2 . Both answers (d) and (e) could be physically meaningful. Answers (a), (b), and (c) must be meaningless since quantities can be added or subtracted only if they have the same dimensions. According to Newton’s second law, Force = mass ? acceleration . Thus, the units of Force must be the product of the units of mass (kg) and the units of acceleration ( m s 2 ). This yields kg ? m s 2, which is answer (a). The calculator gives an answer of 57. 573 for the sum of the 4 given numbers.However, this sum must be rounded to 58 as given in answer (d) so the number of decimal places in the result is the same (zero) as the number of decimal places in the integer 15 (the term in the sum containing the smallest number of decimal places). The required conversion is given by: ? 1 000 mm ? ? 1. 00 cubitus ? h = ( 2. 00 m ) ? ? = 4. 49 cubiti ? 1. 00 m ? ? 445 mm ? This result corresponds to answer (c). 6. The given area (1 420 ft 2 ) contains 3 signi? cant ? gures, assuming that the trailing zero is used only to locate the decimal point. The conversion of this value to square meters is given by: 1. 00 m ? 2 2 2 A = (1. 2 ? 10 3 ft 2 ) ? ? ? = 1. 32 ? 10 m = 132 m ? 3. 281 ft ? Note that the result contains 3 signi? cant ? gures, the same as the number of signi? cant ? gures in the least accurate factor used in the calculation. This result matches answer (b). 7. You cannot add, subtract, or equate a number apples and a number of days. Thus, the answer is yes for (a), (c), and (e). However, you can multiply or divide a number of apples and a number of days. For example, you might divide the number of apples by a number of days to ? nd the number of apples you could eat per day. In summary, the answers are (a) yes, (b) no, (c) yes, (d) no, and (e) es. 2 2. 3. 4. 5. 1 http://helpyoustudy. info 2 Chapter 1 8. The given Cartesian coordinates are x = ? 5. 00, and y = 12. 00 , with the least accurate containing 3 signi? cant ? gures. Note that the speci? ed point (with x < 0 and y > 0 ) is in the second quadrant. The conversion to polar coordinates is then given by: r = x 2 + y 2 = ( ? 5. 00 ) + (12. 00 ) = 13. 0 2 2 tan ? = y 12. 00 = = ? 2. 40 x ? 5. 00 and ? = tan ? 1 ( ? 2. 40 ) = ? 67. 3 ° + 180 ° = 113 ° Note that 180 ° was added in the last step to yield a s econd quadrant angle. The correct answer is therefore (b) (13. 0, 113 °). 9. Doing dimensional analysis on the ? st 4 given choices yields: (a) [ v] ?t ? ? ? 2 = LT L = 3 T2 T (b) [ v] ?x2 ? ? ? = LT = L? 1T ? 1 L2 (c) ? v 2 ? ( L T )2 L2 T 2 L2 ? ?= = = 3 T T T [t ] (d) ? v 2 ? ( L T )2 L2 T 2 L ? ?= = = 2 L L T [ x] Since acceleration has units of length divided by time squared, it is seen that the relation given in answer (d) is consistent with an expression yielding a value for acceleration. 10. The number of gallons of gasoline she can purchase is # gallons = total expenditure 33 Euros ? cost per gallon ? Euros ? ? 1 L ? ? ? 1. 5 L ? ? 1 quart ? ? ? ? ? 5 gal ? 4 quarts ? ? 1 gal ? ? ? ? ? so the correct answer is (b). 1. The situation described is shown in the drawing at the right. h From this, observe that tan 26 ° = , or 45 m h = ( 45 m ) tan 26 ° = 22 m 26 h Thus, the correct answer is (a). 12. 45 m Note that we may write 1. 365 248 0 ? 10 7 as 136. 524 80 ? 10 5. Th us, the raw answer, including the uncertainty, is x = (136. 524 80  ± 2) ? 10 5. Since the ? nal answer should contain all the digits we are sure of and one estimated digit, this result should be rounded and displayed as 137 ? 10 5 = 1. 37 ? 10 7 (we are sure of the 1 and the 3, but have uncertainty about the 7). We see that this answer has three signi? cant ? ures and choice (d) is correct. ANSWERS TO EVEN NUMBERED CONCEPTUAL QUESTIONS 2. Atomic clocks are based on the electromagnetic waves that atoms emit. Also, pulsars are highly regular astronomical clocks. http://helpyoustudy. info Introduction 3 4. (a) (b) (c) ~ 0. 5 lb ? 0. 25 kg or ~10 ? 1 kg ~ 4 lb ? 2 kg or ~10 0 kg ~ 4000 lb ? 2000 kg or ~10 3 kg 6. Let us assume the atoms are solid spheres of diameter 10? 10 m. Then, the volume of each atom is of the order of 10? 30 m3. (More precisely, volume = 4? r 3 3 = ? d 3 6 . ) Therefore, since 1 cm 3 = 10 ? 6 m 3, the number of atoms in the 1 cm3 solid is on the order of 10 ? 1 0 ? 30 = 10 24 atoms. A more precise calculation would require knowledge of the density of the solid and the mass of each atom. However, our estimate agrees with the more precise calculation to within a factor of 10. Realistically, the only lengths you might be able to verify are the length of a football ? eld and the length of a house? y. The only time intervals subject to veri? cation would be the length of a day and the time between normal heartbeats. In the metric system, units differ by powers of ten, so it’s very easy and accurate to convert from one unit to another. 8. 10. ANSWERS TO EVEN NUMBERED PROBLEMS . 4. 6. 8. 10. 12. 14. 16. 18. (a) L T2 (b) L All three equations are dimensionally incorrect. (a) (a) (a) (a) (a) kg ? m s 22. 6 3. 00 ? 108 m s 346 m 2  ± 13 m 2 797 (b) (b) (b) (b) (b) Ft = p 22. 7 2 . 997 9 ? 108 m s 66. 0 m  ± 1. 3 m 1. 1 (c) 17. 66 (c) (c) 22. 6 is more reliable 2. 997 925 ? 108 m s 3. 09 cm s (a) (b) (c) (d) 5. 60 ? 10 2 km = 5. 60 ? 10 5 m = 5. 60 ? 10 7 cm 0. 491 2 km = 491. 2 m = 4. 912 ? 10 4 cm 6. 192 km = 6. 192 ? 10 3 m = 6. 192 ? 10 5 cm 2. 499 km = 2. 499 ? 10 3 m = 2. 499 ? 10 5 cm 20. 22. 24. 26. 10. 6 km L 9. 2 nm s 2 . 9 ? 10 2 m 3 = 2 . 9 ? 108 cm 3 2 . 57 ? 10 6 m 3 ttp://helpyoustudy. info 4 Chapter 1 28. 30. 32. 34. ? 108 steps ~108 people with colds on any given day (a) (a) 4. 2 ? 10 ? 18 m 3 ? 10 29 prokaryotes (b) (b) ~10 ? 1 m 3 ~1014 kg (c) ~1016 cells (c) The very large mass of prokaryotes implies they are important to the biosphere. They are responsible for ? xing carbon, producing oxygen, and breaking up pollutants, among many other biological roles. Humans depend on them! 36. 38. 40. 42. 44. 46. 48. 2. 2 m 8. 1 cm ? s = r12 + r22 ? 2r1r2 cos (? 1 ? ?2 ) 2. 33 m (a) 1. 50 m (b) 2. 60 m 8. 60 m (a) and (b) (c) 50. 52. 54. y= (a) y x = tan 12. 0 °, y ( x ? . 00 km ) = tan 14. 0 ° d ? tan ? ? tan ? tan ? ? tan ? 1. 609 km h (b) 88 km h (d) 1. 44 ? 10 3 m (c) 16 km h Assumes population of 300 million, average of 1 can week per person, and 0. 5 oz per can. (a) ? 1010 cans yr 7. 14 ? 10 ? 2 gal s A2 A1 = 4 ? 10 2 yr (b) (b) (b) (b) ? 10 5 tons yr 2. 70 ? 10 ? 4 m 3 s V2 V1 = 8 ? 10 4 times (c) 1. 03 h 56. 58. 60. 62. (a) (a) (a) ? 10 4 balls yr. Assumes 1 lost ball per hitter, 10 hitters per inning, 9 innings per game, and 81 games per year. http://helpyoustudy. info Introduction 5 PROBLEM SOLUTIONS 1. 1 Substituting dimensions into the given equation T = 2? ionless constant, we have g , and recognizing that 2? is a dimen- [T ] = [ ] [ g] or T= L = L T2 T2 = T Thus, the dimensions are consistent . 1. 2 (a) From x = Bt2, we ? nd that B = [ B] = [ x] L = 2 [t 2 ] T x . Thus, B has units of t2 (b) If x = A sin ( 2? ft ), then [ A] = [ x ] [sin ( 2? ft )] But the sine of an angle is a dimensionless ratio. Therefore, [ A] = [ x ] = L 1. 3 (a) The units of volume, area, and height are: [V ] = L3, [ A] = L2 , and [h] = L We then observe that L3 = L2 L or [V ] = [ A][h] Thus, the equation V = Ah is dimensionally correct . (b) Vcylinder = ? R 2 h = (? R 2 ) h = Ah , where A = ?R 2 Vrectangular box = wh = ( w ) h = Ah, where A = w = length ? width 1. 4 (a) L ML2 2 2 m v 2 = 1 m v0 + mgh, [ m v 2 ] = [ m v0 ] = M ? ? = 2 ? ? 2 T ? T? 1 2 L ? M L while ? mgh ? = M ? 2 ? L = . Thus, the equation is dimensionally incorrect . ? ? ? T ? T ? In the equation 1 2 2 (b) L L but [at 2 ] = [a][t 2 ] = ? 2 ? ( T 2 ) = L. Hence, this equation ? ? T ? T ? is dimensionally incorrect . In v = v0 + at 2, [ v] = [ v0 ] = L In the equation ma = v 2, we see that [ ma] = [ m][a] = M ? 2 ? ?T Therefore, this equation is also dimensionally incorrect . 2 ? = ML , while [ v 2 ] = ? L ? = L . ? ? ? 2 T2 ? T ? T? 2 (c) . 5 From the universal gravitation law, the constant G is G = Fr 2 Mm. Its units are then [G ] = [ F ] ? r 2 ? ( kg ? m s2 ) ( m 2 ) m3 ? ?= = kg ? kg kg ? s 2 [ M ][ m ] http://helpyoustudy. info 6 Chapter 1 1. 6 (a) Solving KE = p2 for the momentum, p, gives p = 2 m ( K E ) where the numeral 2 is a 2m dimensionless constant. Dimensional analysis gives the units of momentum as: [ p] = [ m ][ KE ] = M ( M ? L2 T 2 ) = M 2 ? L2 T 2 = M ( L T ) Therefore, in the SI system, the units of momentum are kg ? ( m s ) . (b) Note that the units of force are kg ? m s 2 or [ F ] = M ? L T 2 . Then, observe that [ F ][ t ] = ( M ?L T 2 ) ? T = M ( L T ) = [ p ] From this, it follows that force multiplied by time is proportional to momentum: Ft = p . (See the impulse–momentum theorem in Chapter 6, F ? ?t = ? p , which says that a constant force F multiplied by a duration of time ? t equals the change in momentum, ? p. ) 1. 7 1. 8 Area = ( length ) ? ( width ) = ( 9. 72 m )( 5. 3 m ) = 52 m 2 (a) Computing ( 8) 3 without rounding the intermediate result yields ( 8) (b) 3 = 22. 6 to three signi? cant ? gures. Rounding the intermediate result to three signi? cant ? gures yields 8 = 2. 8284 > 2. 83 Then, we obtain ( 8) 3 = ( 2. 83) = 22. 7 to three signi? ant ? gures. 3 (c) 1. 9 (a) (b) (c) (d) The answer 22. 6 is more reliable because rounding in part (b) was carried out too soon. 78. 9  ± 0. 2 has 3 significant figures with the uncertainty in the tenths position. 3. 788 ? 10 9 has 4 significant figures 2. 46 ? 10 ? 6 has 3 significant figures 0. 003 2 = 3. 2 ? 10 ? 3 has 2 significant figures . The two zeros were originally included only to position the decimal. 1. 10 c = 2 . 997 924 58 ? 108 m s (a) (b) (c) Rounded to 3 signi? cant ? gures: c = 3. 00 ? 108 m s Rounded to 5 signi? cant ? gures: c = 2 . 997 9 ? 108 m s Rounded to 7 signi? cant ? gures: c = 2 . 997 925 ? 08 m s 1. 11 Observe that the length = 5. 62 cm, the width w = 6. 35 cm, and the height h = 2. 78 cm all contain 3 signi? cant ? gures. Thus, any product of these quantities should contain 3 signi? cant ? gures. (a) (b) w = ( 5. 62 cm )( 6. 35 cm ) = 35. 7 cm 2 V = ( w ) h = ( 35. 7 cm 2 ) ( 2. 78 cm ) = 99. 2 cm 3 continued on next page http://helpyoustudy. info Introd uction 7 (c) wh = ( 6. 35 cm )( 2. 78 cm ) = 17. 7 cm 2 V = ( wh ) = (17. 7 cm 2 ) ( 5. 62 cm ) = 99. 5 cm 3 (d) In the rounding process, small amounts are either added to or subtracted from an answer to satisfy the rules of signi? cant ? gures.For a given rounding, different small adjustments are made, introducing a certain amount of randomness in the last signi? cant digit of the ? nal answer. 2 2 2 A = ? r 2 = ? (10. 5 m  ± 0. 2 m ) = ? ?(10. 5 m )  ± 2 (10. 5 m )( 0. 2 m ) + ( 0. 2 m ) ? ? ? 1. 12 (a) Recognize that the last term in the brackets is insigni? cant in comparison to the other two. Thus, we have A = ? ?110 m 2  ± 4. 2 m 2 ? = 346 m 2  ± 13 m 2 ? ? (b) 1. 13 C = 2? r = 2? (10. 5 m  ± 0. 2 m ) = 66. 0 m  ± 1. 3 m The least accurate dimension of the box has two signi? cant ? gures. Thus, the volume (product of the three dimensions) will contain only two signi? cant ? ures. V = ? w ? h = ( 29 cm )(17. 8 cm )(11. 4 cm ) = 5. 9 ? 10 3 cm 3 1. 14 (a) The sum is rounded to 797 because 756 in the terms to be added has no positions beyond the decimal. 0. 003 2 ? 356. 3 = ( 3. 2 ? 10 ? 3 ) ? 356. 3 = 1. 14016 must be rounded to 1. 1 because 3. 2 ? 10 ? 3 has only two signi? cant ? gures. 5. 620 ? ? must be rounded to 17. 66 because 5. 620 has only four signi? cant ? gures. (b) (c) 1. 15 5 280 ft ? ? 1 fathom ? 8 d = ( 250 000 mi ) ? ? ? = 2 ? 10 fathoms ? 1. 000 mi ? ? 6 ft ? The answer is limited to one signi? cant ? gure because of the accuracy to which the conversion from fathoms to feet is given. . 16 v= t = 186 furlongs 1 fortnight ? 1 fortnight ? ? 14 days ? ? ? 1 day ? ? 220 yds ? ? 8. 64 ? 10 4 s ? ? 1 furlong ? ? 3 ft ? ? 1 yd ? ? 100 cm ? ? ? 3. 281 ft ? ? ? giving v = 3. 09 cm s ? ? 3. 786 L ? ? 1 gal ? ? 10 3 cm 3 ? ? 1 m 3 ? = 0. 204 m 3 ? ? 1 L ? ? 10 6 cm 3 ? ? ? 1. 17 ? 9 gal 6. 00 firkins = 6. 00 firkins ? ? 1 firkin ? (a) 1. 18 1. 609 km ? 2 5 7 = ( 348 mi ) ? 6 ? ? = 5. 60 ? 10 km = 5. 60 ? 10 m = 5. 60 ? 10 cm ? 1. 000 mi ? ? 1. 609 km ? 4 h = (1 612 ft ) ? 2 ? = 0. 491 2 km = 491. 2 m = 4. 912 ? 10 cm 5 280 ft ? ? ? 1. 609 km ? 3 5 h = ( 20 320 ft ) ? = 6. 192 km = 6. 192 ? 10 m = 6. 192 ? 10 cm 5 280 ft ? ? (b) (c) continued on next page http://helpyoustudy. info 8 Chapter 1 (d) ? 1. 609 km ? 3 5 d = (8 200 ft ) ? ? = 2 . 499 km = 2 . 499 ? 10 m = 2 . 499 ? 10 cm ? 5 280 ft ? In (a), the answer is limited to three signi? cant ? gures because of the accuracy of the original data value, 348 miles. In (b), (c), and (d), the answers are limited to four signi? cant ? gures because of the accuracy to which the kilometers-to-feet conversion factor is given. 1. 19 v = 38. 0 m ? 1 km ? ? 1 mi ? ? 3 600 s ? ? = 85. 0 mi h ? s ? 10 3 m ? ? 1. 609 km ? 1 h ? Yes, the driver is exceeding the speed limit by 10. 0 mi h . mi ? 1 km ? ? 1 gal ? ? = 10. 6 km L ? gal ? 0. 621 mi ? ? 3. 786 L ? ? ? 1. 20 efficiency = 25. 0 r= 1. 21 (a) (b) (c) diameter 5. 36 in ? 2. 54 cm ? = ? ? = 6. 81 cm 2 2 ? 1 in ? 2 A = 4? r 2 = 4? ( 6. 81 cm ) = 5. 83 ? 10 2 cm 2 V= 4 3 4 3 ? r = ? ( 6. 81 cm ) = 1. 32 ? 10 3 cm 3 3 3 ? ? 1 h ? ? 2. 54 cm ? ? 10 9 nm ? ? 3 600 s ? ? 1. 00 in ? ? 10 2 cm ? = 9. 2 nm s ? 1. 22 ? 1 in ? ? 1 day rate = ? ? 32 day ? ? 24 h ? This means that the proteins are assembled at a rate of many layers of atoms each second! 1. 3 ? m ? ? 3 600 s ? ? 1 km ? ? 1 mi ? 8 c = ? 3. 00 ? 10 8 ? = 6. 71 ? 10 mi h s ? ? 1 h ? ? 10 3 m ? ? 1. 609 km ? ? ? 2 . 832 ? 10 ? 2 m3 ? Volume of house = ( 50. 0 ft )( 26 ft )(8. 0 ft ) ? ? 1 ft 3 ? ? ? 100 cm ? = 2 . 9 ? 10 2 m3 = ( 2 . 9 ? 10 2 m3 ) ? = 2 . 9 ? 10 8 cm3 ? 1m ? ? 1. 25 1. 26 2 2 ? 1 m ? 43 560 ft ? ? 1 m ? ? ? = 3. 08 ? 10 4 m3 Volume = 25. 0 acre ft ? ? ? ? ? 3. 281 ft ? 1 acre ? ? 3. 281 ft ? ? ? ? ? 1 Volume of pyramid = ( area of base )( height ) 3 3 1. 24 ( ) = 1 ? (13. 0 acres )( 43 560 ft 2 acre ) ? ( 481 ft ) = 9. 08 ? 10 7 f ? 3? ? 2 . 832 ? 10 ? 2 m3 ? 3 = ( 9. 08 ? 10 7 ft 3 ) ? 5 ? = 2 . 57 ? 10 m 1 ft3 ? ? 1. 27 Volume of cube = L 3 = 1 quart (Where L = length of one side of the cube. ) ? 1 gallon ? ? 3. 786 liter ? ? 1000 cm3 ? i = 947 cm3 Thus, L 3 = 1 quart ? ? 4 quarts ? ? 1 gallon ? ? 1 liter ? ? ? ? ( ) and L = 3 947 cm3 = 9. 82 cm http://helpyoustudy. info Introduction 9 1. 28 We estimate that the length of a step for an average person is about 18 inches, or roughly 0. 5 m. Then, an estimate for the number of steps required to travel a distance equal to the circumference of the Earth would be N= or 3 2? ( 6. 38 ? 10 6 m ) Circumference 2?RE = ? ? 8 ? 10 7 steps 0. 5 m step Step Length Step Length N ? 108 steps 1. 29. We assume an average respiration rate of about 10 breaths/minute and a typical life span of 70 years. Then, an estimate of the number of breaths an average person would take in a lifetime is ? ? breaths ? 10 7 ? min n = ? 10 ( 70 yr ) ? 3. 156 ? yr s ? ? 160 s ? = 4 ? 108 breaths ? ? ? min ? 1 ? ? ? or n ? 108 breaths 1. 30 We assume that the average person catches a cold twice a year and is sick an average of 7 days (or 1 week) each time. Thus, on average, each person is sick for 2 weeks out of each year (52 weeks).The probability that a particular person will be sick at any given time equals the percentage of time that person is sick, or probability of sickness = 2 weeks 1 = 52 weeks 26 The population of the Earth is approximately 7 billion. The number of people expected to have a cold on any given day is then 1 Number sick = ( population )( probability of sickness ) = ( 7 ? 10 9 ) ? ? = 3 ? 108 or ? 108 ( ? ? ? 26 ? 1. 31 (a) Assume that a typical intestinal tract has a length of about 7 m and average diameter of 4 cm. The estimated total intestinal volume is then ? ?d 2 ? ? ( 0. 04 m ) Vtotal = A = ? ( 7 m ) = 0. 009 m 3 ? 4 ? 4 ? 2 The approximate volume occupied by a single bacterium is Vbacteria ? ( typical length scale ) = (10 ? 6 m ) = 10 ? 18 m 3 3 3 If it is assumed that bacteria occupy one hundredth of the total intestinal volume, the estimate of the number of microorganisms in the human intestinal tract is n= (b) 3 Vtotal 100 ( 0. 009 m ) 100 = = 9 ? 1013 or n ? 1014 10 ? 18 m 3 Vbacteria The large value of the number of bacteria estimated to exist in the intestinal tract means that they are probably not dangerous. Intestinal bacteria help digest food and provide important nutrients. Humans and bacteria enjoy a mutually bene? ial symbiotic relationship. Vcell = 3 4 3 4 ? r = ? (1. 0 ? 10 ? 6 m ) = 4. 2 ? 10 ? 18 m 3 3 3 1. 32 (a) (b) Consider your body to be a cylinder having a radius of about 6 inches (or 0. 15 m) and a height of about 1. 5 meters. Then, its volume is Vbody = Ah = (? r 2 ) h = ? ( 0. 15 m ) (1. 5 m ) = 0. 11 m 3 or ? 10 ? 1 m 3 2 continued on next page http://helpyoustudy. info 10 Chapter 1 (c) The estimate of the number of cells in the body is then n= Vbody Vcell = 0. 11 m 3 = 2. 6 ? 1016 or ? 1016 ? 18 3 4. 2 ? 10 m 1. 33 A reasonable guess for the diameter of a tire might be 3 f t, with a circumference (C = 2? r = ?D = distance travels per revolution) of about 9 ft. Thus, the total number of revolutions the tire might make is n= total distance traveled ( 50 000 mi )( 5 280 ft mi ) = 3 ? 10 7 rev, or ~ 10 7 rev = distance per revolution 9 ft rev 1. 34 Answers to this problem will vary, dependent on the assumptions one makes. This solution assumes that bacteria and other prokaryotes occupy approximately one ten-millionth (10? 7) of the Earth’s volume, and that the density of a prokaryote, like the density of the human body, is approximately equal to that of water (103 kg/m3). (a) estimated number = n = Vtotal Vsingle prokaryote 10 )V ? ?7 Earth Vsingle prokaryote (10 )(10 m ) ? ? (length scale) (10 m ) ?7 3 Earth ? 7 6 3 ? 6 3 (10 ) R 3 ? 10 29 (b) (c) 3 kg ? ? ? ? mtotal = ( density )( total volume) ? ?water ? nVsingle ? = ? 10 3 3 ? (10 29 )(10 ? 6 m ) ? 1014 kg ? ? prokaryote ? ? m The very large mass of prokaryotes implies they are important to the biosphere. They are responsible for ? xing carbon, producing oxygen, and breaking up pollutants, among many other biological roles. Humans depend on them! x = r cos? = 2 . 5 m cos 35 ° = 2. 0 m 1. 35 The x coordinate is found as and the y coordinate ) y = r sin? = ( 2 . 5 m ) sin 35 ° = 1. m ( 2 1. 36 The x distance out to the ? y is 2. 0 m and the y distance up to the ? y is 1. 0 m. Thus, we can use the Pythagorean theorem to ? nd the distance from the origin to the ? y as d = x 2 + y2 = ( 2. 0 m ) + (1. 0 m ) 2 = 2. 2 m 1. 37 The distance from the origin to the ? y is r in polar coordinates, and this was found to be 2. 2 m in Problem 36. The angle ? is the angle between r and the horizontal reference line (the x axis in this case). Thus, the angle can be found as tan ? = y 1. 0 m = = 0. 50 x 2. 0 m and ? = tan ? 1 ( 0. 50 ) = 27 ° The polar coordinates are r = 2. 2 m and ? = 27  ° 1. 8 The x distance between the two points is ? x = x2 ? x1 = ? 3. 0 cm ? 5. 0 cm = 8. 0 cm and the y distance between them is ? y = y2 ? y1 = 3. 0 cm ? 4. 0 cm = 1. 0 cm. The distance between them is found from the Pythagorean theorem: d= 1. 39 ? x + ? y = (8. 0 cm ) + (1. 0 cm ) = 2 2 2 2 65 cm 2 = 8. 1 cm Refer to the Figure given in Problem 1. 40 below. The Cartesian coordinates for the two given points are: x1 = r1 cos ? 1 = ( 2. 00 m ) cos 50. 0 ° = 1. 29 m y1 = r1 sin ? 1 = ( 2. 00 m ) sin 50. 0 ° = 1. 53 m x2 = r2 cos ? 2 = ( 5. 00 m ) cos ( ? 50. 0 °) = 3. 21 m y2 = r2 sin ? 2 = ( 5. 00 m ) sin ( ? 50. 0 °) = ? 3. 3 m continued on next page http://helpyoustudy. info Introduction 11 The distance between the two points is then: ? s = ( ? x ) + ( ? y ) = (1. 29 m ? 3. 21 m ) + (1. 53 m + 3. 83 m ) = 5. 69 m 2 2 2 2 1. 40 Consider the Figure shown at the right. The Cartesian coordinates for the two points are: x1 = r1 cos ? 1 y1 = r1 sin ? 1 x2 = r2 cos ? 2 y2 = r2 sin ? 2 y (x1, y1) r1 ?s ?y y1 y2 The distance between the two points is the length of the hypot enuse of the shaded triangle and is given by ? s = ( ? x ) + ( ? y ) = 2 2 q1 ( x1 ? x2 ) + ( y1 ? y2 ) 2 2 (x2, y2) r2 ? x q2 x1 x2 x or ? s = (r 2 1 cos 2 ? 1 + r22 cos 2 ? ? 2r1r2 cos ? 1 cos ? 2 ) + ( r12 sin 2 ? 1 + r22 sin 2 ? 2 ? 2r1r2 sin ? 1 sin ? 2 ) = r12 ( cos 2 ? 1 + sin 2 ? 1 ) + r22 ( cos 2 ? 2 + sin 2 ? 2 ) ? 2r1r2 ( cos ? 1 cos ? 2 + sin ? 1 sin ? 2 ) i Applying the identities cos 2 ? + sin 2 ? = 1 and cos ? 1 cos ? 2 + sin ? 1 sin ? 2 = cos (? 1 ? ?2 ) , this reduces to ? s = r12 + r22 ? 2r1r2 ( cos ? 1 cos ? 2 + sin ? 1 sin ? 2 ) = 1. 41 (a) r12 + r22 ? 2r1r2 cos (? 1 ? ?2 ) With a = 6. 00 m and b being two sides of this right triangle having hypotenuse c = 9. 00 m, the Pythagorean theorem gives the unknown side as b = c2 ? a2 = ( 9. 00 m )2 ? ( 6. 00 m )2 = 6. 1 m (c) sin ? = b 6. 71 m = = 0. 746 c 9. 00 m (b) tan ? = a 6. 00 m = = 0. 894 b 6. 71 m 1. 42 From the diagram, cos ( 75. 0 °) = d L Thus, d = L cos ( 75. 0 °) = ( 9. 00 m ) cos ( 75. 0 °) = 2. 33 m L 9 . 00 m 75. 0 d http://helpyoustudy. info 12 Chapter 1 1. 43 The circumference of the fountain is C = 2? r , so the radius is C 15. 0 m = = 2. 39 m 2? 2? h h Thus, tan ( 55. 0 °) = = which gives r 2. 39 m r= h = ( 2. 39 m ) tan ( 55. 0 °) = 3. 41 m 1. 44 (a) (b) sin ? = cos ? = opposite side so, opposite side = ( 3. 00 m ) sin ( 30. 0 ° ) = 1. 50 m hypotenuse adjacent side so, adjacent side = ( 3. 00 m ) cos ( 30.  ° ) = 2 . 60 m hypotenuse (b) (d) The side adjacent to ? = 3. 00 sin ? = 4. 00 = 0. 800 5. 00 1. 45 (a) (c) (e) The side opposite ? = 3. 00 cos ? = tan ? = 4. 00 = 0. 800 5. 00 4. 00 = 1. 33 3. 00 1. 46 Using the diagram at the right, the Pythagorean theorem yields c = ( 5. 00 m ) + ( 7. 00 m ) = 8. 60 m 2 2 5. 00 m c q 7. 00 m 1. 47 From the diagram given in Problem 1. 46 above, it is seen that tan ? = 5. 00 = 0. 714 7. 00 and ? = tan ? 1 ( 0. 714 ) = 35. 5 ° 1. 48 (a) and (b) (c) See the Figure given at the right. Applying the de? nition of the tangent fun ction to the large right triangle containing the 12.  ° angle gives: y x = tan 12. 0 ° [1] Also, applying the de? nition of the tangent function to the smaller right triangle containing the 14. 0 ° angle gives: y = tan 14. 0 ° x ? 1. 00 km (d) From Equation [1] above, observe that x = y tan 12. 0 ° [2] Substituting this result into Equation [2] gives y ? tan 12. 0 ° = tan 14. 0 ° y ? (1. 00 km ) tan 12. 0 ° continued on next page http://helpyoustudy. info Introduction 13 Then, solving for the height of the mountain, y, yields y= 1. 49 (1. 00 km ) tan 12. 0 ° tan 14. 0 ° tan 14. 0 ° ? tan 12. 0 ° = 1. 44 km = 1. 44 ? 10 3 m Using the sketch at the right: w = tan 35.  ° , or 100 m w = (100 m ) tan 35. 0 ° = 70. 0 m w 1. 50 The ? gure at the right shows the situation described in the problem statement. Applying the de? nition of the tangent function to the large right triangle containing the angle ? in the Figure, one obtains y x = tan ? Also, applying the d e? nition of the tangent function to the small right triangle containing the angle ? gives y = tan ? x? d Solving Equation [1] for x and substituting the result into Equation [2] yields y = tan ? y tan ? ? d The last result simpli? es to or y ? tan ? = tan ? y ? d ? tan ? y ? tan ? = y ? tan ? ? d ? tan ? ? tan ? or [2] [1]Solving for y: y ( tan ? ? tan ? ) = ? d ? tan ? ? tan ? y=? 1. 51 (a) d ? tan ? ? tan ? d ? tan ? ? tan ? = tan ? ? tan ? tan ? ? tan ? Given that a ? F m , we have F ? ma . Therefore, the units of force are those of ma, [ F ] = [ ma] = [ m][a] = M ( L T 2 ) = M L T-2 (b) L M? L [F ] = M ? 2 ? = 2 ? ? T ? T ? 1 so newton = kg ? m s2 1. 52 (a) mi ? mi ? ? 1. 609 km ? km = ? 1 ? = 1. 609 h ? h ? ? 1 mi ? h mi ? mi ? ? 1. 609 km h ? km = ? 55 ? = 88 h ? h ? ? 1 mi h ? h mi mi ? mi ? ? 1. 609 km h ? km ? 55 = ? 10 ? = 16 h h ? h ? ? 1 mi h ? h (b) vmax = 55 (c) ?vmax = 65 http://helpyoustudy. info 14 Chapter 1 1. 3 (a) Since 1 m = 10 2 cm , then 1 m 3 = (1 m ) = ( 10 2 cm ) = (10 2 ) cm 3 = 10 6 cm 3, giving 3 3 3 ? 1. 0 ? 10 ? 3 kg ? 3 mass = density volume = ? ? 1. 0 m 3 ? 1. 0 cm ? ( )( ) ( ) ? 10 6 cm3 ? ? kg ? 3 = ? 1. 0 ? 10 ? 3 3 ? 1. 0 m 3 ? ? = 1. 0 ? 10 kg 3 ? cm ? ? 1m ? ( ) As a rough calculation, treat each of the following objects as if they were 100% water. (b) (c) (d) 3 kg 4 cell: mass = density ? volume = ? 10 3 3 ? ? ( 0. 50 ? 10 ? 6 m ) = 5. 2 ? 10 ? 16 kg ? ? m ? 3 ? 3 4 kg 4 kidney: mass = density ? volume = ? ? ? r 3 ? = ? 10 3 3 ? ? ( 4. 0 ? 10 ? 2 m ) = 0. 27 kg ? ? ? ? m ? 3 ? 3 ? ? ?y: mass = density ? olume = ( density ) (? r 2 h ) 2 kg = ? 10 3 3 ? ? (1. 0 ? 10 ? 3 m ) ( 4. 0 ? 10 ? 3 m ) = 1. 3 ? 10 ? 5 kg ? ? m ? ? 1. 54 Assume an average of 1 can per person each week and a population of 300 million. (a) number cans person ? number cans year = ? ? ? ( population )( weeks year ) week ? ? ? ?1 ? ? can person ? 8 ? ( 3 ? 10 people ) ( 52 weeks yr ) week ? ? 2 ? 1010 cans yr , or ~10 10 cans yr (b) number of tons = ( weight can )( number cans year ) ? oz ? ? 1 lb ? ? 1 ton ? 10 can ? ? 0. 5 ? ? 2 ? 10 ? can ? ? 16 oz ? ? 2 000 lb ? yr ? ? 3 ? 10 5 ton yr , or ~10 5 ton yr Assumes an average weight of 0. oz of aluminum per can. 1. 55 The term s has dimensions of L, a has dimensions of LT? 2, and t has dimensions of T. Therefore, the equation, s = k a m t n with k being dimensionless, has dimensions of L = ( LT ? 2 ) ( T ) m n or L1T 0 = L m T n? 2 m The powers of L and T must be the same on each side of the equation. Therefore, L1 = Lm and m =1 Likewise, equating powers of T, we see that n ? 2 m = 0, or n = 2 m = 2 Dimensional analysis cannot determine the value of k , a dimensionless constant. 1. 56 (a) The rate of ? lling in gallons per second is rate = 30. 0 gal ? 1 min ? ?2 ? ? = 7. 14 ? 10 gal s 7. 0 min ? 60 s ? continued on next page http://helpyoustudy. info Introduction 15 (b) 3 1L Note that 1 m 3 = (10 2 cm ) = (10 6 cm 3 ) ? 3 ? 3 ? 10 cm ? = 10 3 L. Thus, ? ? rate = 7. 14 ? 10 ? 2 (c) t= gal ? 3. 786 L ? ? 1 m 3 ? ?4 3 ? ? = 2. 70 ? 10 m s s ? 1 gal ? ? 10 3 L ? ? 1h ? Vfilled 1. 00 m 3 = = 3. 70 ? 10 3 s ? ? = 1. 03 h ? 4 3 rate 2. 70 ? 10 m s ? 3 600 s ? 1. 57 The volume of paint used is given by V = Ah, where A is the area covered and h is the thickness of the layer. Thus, h= V 3. 79 ? 10 ? 3 m 3 = = 1. 52 ? 10 ? 4 m = 152 ? 10 ? 6 m = 152 ? m 25. 0 m 2 A 1. 58 (a) For a sphere, A = 4? R 2 .In this case, the radius of the second sphere is twice that of the ? rst, or R2 = 2 R1. Hence, A2 4? R 2 R 2 ( 2 R1 ) 2 = = 2 = = 4 2 2 A1 4? R 1 R 1 R12 2 (b) For a sphere, the volume is Thus, V= 4 3 ? R 3 3 V2 ( 4 3) ? R 3 R 3 ( 2 R1 ) 2 = = 2 = = 8 3 3 3 V1 ( 4 3) ? R 1 R 1 R1 1. 59 The estimate of the total distance cars are driven each year is d = ( cars in use ) ( distance traveled per car ) = (100 ? 10 6 cars )(10 4 mi car ) = 1 ? 1012 mi At a rate of 20 mi/gal, the fuel used per year would be V1 = d 1 ? 1012 mi = = 5 ? 1010 gal rate1 20 mi gal If the rate increased to 25 mi gal, the annual fuel consumption would be V2 = d 1 ? 012 mi = = 4 ? 1010 gal rate2 25 mi gal and the fuel savings each year would be savings = V1 ? V2 = 5 ? 1010 gal ? 4 ? 1010 gal = 1 ? 1010 gal 1. 60 (a) The amount paid per year would be dollars ? ? 8. 64 ? 10 4 s ? ? 365. 25 days ? 10 dollars annual amount = ? 1 000 ? ? = 3. 16 ? 10 s ? ? 1. 00 day ? ? yr yr ? ? Therefore, it would take (b) 10 ? 10 12 dollars = 3 ? 10 2 yr, 3. 16 ? 10 10 dollars yr or ~10 2 yr The circumference of the Earth at the equator is C = 2? r = 2? 6. 378 ? 10 6 m = 4. 007 ? 10 7 m ( ) continued on next page http://helpyoustudy. info 16 Chapter 1 The length of one dollar bill is 0. 55 m, so the length of ten trillion bills is m ? 12 12 = ? 0. 155 ? ? (10 ? 10 dollars ) = 1? 10 m. Thus, the ten trillion dollars would dollar ? ? encircle the Earth 1 ? 1012 m n= = = 2 ? 10 4 , or ~10 4 times C 4. 007 ? 10 7 m 1. 61 (a) (b) ? 365. 2 days ? ? 8. 64 ? 10 4 s ? 1 yr = (1 yr ) ? = 3. 16 ? 10 7 s ? ? ? 1 day ? 1 yr ? ? ? Consider a segment of the surface of the Moon which has an area of 1 m2 and a depth of 1 m. When ? lled with meteorites, each having a diameter 10? 6 m, the number of meteorites along each edge of this box is n= length of an edge 1m = = 10 6 meteorite diameter 10 ? 6 m The total number of meteorites in the ? led box is then N = n 3 = 10 6 3 = 10 18 At the rate of 1 meteorite per second, the time to ? ll the box is 1y ? = 3 ? 10 10 yr, or t = 1018 s = (1018 s ) ? ? ? 7 ? 3. 16 ? 10 s ? 1. 62 ~1010 yr ( ) We will assume that, on average, 1 ball will be lost per hitter, that there will be about 10 hitters per inning, a game has 9 innings, and the team plays 81 home games per season. Our estimate of the number of game balls needed per season is then number of balls needed = ( number lost per hitter ) ( number hitters/game )( home games/year ) games ? hitters ? ? innings ? = (1 ball per hitter ) 10 ? 81 ? ? ? year ? inning ? ? game ? = 7300 balls year o r ~10 4 balls year 1. 63 The volume of the Milky Way galaxy is roughly ? ?d2 ? ? VG = At = ? t ? 10 21 m 4 ? 4 ? ? ( ) (10 m ) 2 19 or VG ? 10 61 m3 r If, within the Milky Way galaxy, there is typically one neutron star in a spherical volume of radius r = 3 ? 1018 m, then the galactic volume per neutron star is V1 = 3 4 3 4 ? r = ? ( 3 ? 1018 m ) = 1 ? 10 56 m 3 3 3 or V1 ? 10 56 m 3 The order of magnitude of the number of neutron stars in the Milky Way is then n= VG 10 61 m 3 ? V1 10 56 m 3 or n ? 10 5 neutron stars http://helpyoustudy. info 2 Motion in One DimensionQUICK QUIZZES 1. 2. (a) (a) 200 yd (b) 0 (c) 0 False. The car may be slowing down, so that the direction of its acceleration is opposite the direction of its velocity. True. If the velocity is in the direction chosen as negative, a positive acceleration causes a decrease in speed. True. For an accelerating particle to stop at all, the velocity and acceleration must have opposite signs, so that the speed is decreasing. I f this is the case, the particle will eventually come to rest. If the acceleration remains constant, however, the particle must begin to move again, opposite to the direction of its original velocity.If the particle comes to rest and then stays at rest, the acceleration has become zero at the moment the motion stops. This is the case for a braking car—the acceleration is negative and goes to zero as the car comes to rest. (b) (c) 3. The velocity-vs. -time graph (a) has a constant slope, indicating a constant acceleration, which is represented by the acceleration-vs. -time graph (e). Graph (b) represents an object whose speed always increases, and does so at an ever increasing rate. Thus, the acceleration must be increasing, and the acceleration-vs. -time graph that best indicates this behavior is (d).Graph (c) depicts an object which ? rst has a velocity that increases at a constant rate, which means that the object’s acceleration is constant. The motion then changes t o one at constant speed, indicating that the acceleration of the object becomes zero. Thus, the best match to this situation is graph (f). 4. Choice (b). According to graph b, there are some instants in time when the object is simultaneously at two different x-coordinates. This is physically impossible. (a) The blue graph of Figure 2. 14b best shows the puck’s position as a function of time. As seen in Figure 2. 4a, the distance the puck has traveled grows at an increasing rate for approximately three time intervals, grows at a steady rate for about four time intervals, and then grows at a diminishing rate for the last two intervals. The red graph of Figure 2. 14c best illustrates the speed (distance traveled per time interval) of the puck as a function of time. It shows the puck gaining speed for approximately three time intervals, moving at constant speed for about four time intervals, then slowing to rest during the last two intervals. 5. (b) 17 http://helpyoustudy. info 1 8 Chapter 2 (c) The green graph of Figure 2. 4d best shows the puck’s acceleration as a function of time. The puck gains velocity (positive acceleration) for approximately three time intervals, moves at constant velocity (zero acceleration) for about four time intervals, and then loses velocity (negative acceleration) for roughly the last two time intervals. 6. Choice (e). The acceleration of the ball remains constant while it is in the air. The magnitude of its acceleration is the free-fall acceleration, g = 9. 80 m/s2. Choice (c). As it travels upward, its speed decreases by 9. 80 m/s during each second of its motion. When it reaches the peak of its motion, its speed becomes zero.As the ball moves downward, its speed increases by 9. 80 m/s each second. Choices (a) and (f). The ? rst jumper will always be moving with a higher velocity than the second. Thus, in a given time interval, the ? rst jumper covers more distance than the second, and the separation distance between th em increases. At any given instant of time, the velocities of the jumpers are de? nitely different, because one had a head start. In a time interval after this instant, however, each jumper increases his or her velocity by the same amount, because they have the same acceleration. Thus, the difference in velocities stays the same. . 8. ANSWERS TO MULTIPLE CHOICE QUESTIONS 1. Once the arrow has left the bow, it has a constant downward acceleration equal to the freefall acceleration, g. Taking upward as the positive direction, the elapsed time required for the velocity to change from an initial value of 15. 0 m s upward ( v0 = +15. 0 m s ) to a value of 8. 00 m s downward ( v f = ? 8. 00 m s ) is given by ? t = ? v v f ? v0 ? 8. 00 m s ? ( +15. 0 m s ) = = = 2. 35 s a ? g ? 9. 80 m s 2 Thus, the correct choice is (d). 2. In Figure MCQ2. 2, there are ? ve spaces separating adjacent oil drops, and these spaces span a distance of ? x = 600 meters.Since the drops occur every 5. 0 s, the ti me span of each space is 5. 0 s and the total time interval shown in the ? gure is ? t = 5 ( 5. 0 s ) = 25 s. The average speed of the car is then v= ? x 600 m = = 24 m s ? t 25 s making (b) the correct choice. 3. The derivation of the equations of kinematics for an object moving in one dimension (Equations 2. 6 through 2. 10 in the textbook) was based on the assumption that the object had a constant acceleration. Thus, (b) is the correct answer. An object having constant acceleration would have constant velocity only if that acceleration had a value of zero, so (a) is not a necessary condition.The speed (magnitude of the velocity) will increase in time only in cases when the velocity is in the same direction as the constant acceleration, so (c) is not a correct response. An object projected straight upward into the air has a constant acceleration. Yet its position (altitude) does not always increase in time (it eventually starts to fall back downward) nor is its velocity always dir ected downward (the direction of the constant acceleration). Thus, neither (d) nor (e) can be correct. http://helpyoustudy. info Motion in One Dimension 19 4. The bowling pin has a constant downward acceleration ( a = ? g = ? 9. 80 m s 2 ) while in ? ght. The velocity of the pin is directed upward on the upward part of its ? ight and is directed downward as it falls back toward the juggler’s hand. Thus, only (d) is a true statement. The initial velocity of the car is v0 = 0 and the velocity at time t is v. The constant acceleration is therefore given by a = ? v ? t = ( v ? v0 ) t = ( v ? 0 ) t = v t and the average velocity of the car is v = ( v + v0 ) 2 = ( v + 0 ) 2 = v 2. The distance traveled in time t is ? x = vt = vt 2. In the special case where a = 0 ( and hence v = v0 = 0 ) , we see that statements (a), (b), (c), and (d) are all correct. However, in the general case ( a ? , and hence v ? 0 ), only statements (b) and (c) are true. Statement (e) is not true in either ca se. The motion of the boat is very similar to that of a object thrown straight upward into the air. In both cases, the object has a constant acceleration which is directed opposite to the direction of the initial velocity. Just as the object thrown upward slows down and stops momentarily before it starts speeding up as it falls back downward, the boat will continue to move northward for some time, slowing uniformly until it comes to a momentary stop. It will then start to move in the southward direction, gaining speed as it goes.The correct answer is (c). In a position versus time graph, the velocity of the object at any point in time is the slope of the line tangent to the graph at that instant in time. The speed of the particle at this point in time is simply the magnitude (or absolute value) of the velocity at this instant in time. The displacement occurring during a time interval is equal to the difference in x-coordinates at the ? nal and initial times of the interval ? x = x t f ? x ti . 5. 6. 7. ( ) The average velocity during a time interval is the slope of the straight line connecting the points on the curve corresponding to the initial and ? al times of the interval ? v = ? x ? t = ( x f ? xi ) ( t f ? ti ) ? . Thus, we see how the quantities in choices (a), (e), (c), and (d) ? ? can all be obtained from the graph. Only the acceleration, choice (b), cannot be obtained from the position versus time graph. 8. From ? x = v0 t + 1 at 2, the distance traveled in time t, starting from rest ( v0 = 0 ) with constant 2 acceleration a, is ? x = 1 at 2 . Thus, the ratio of the distances traveled in two individual trials, one 2 of duration t1 = 6 s and the second of duration t 2 = 2 s, is 2 2 ? x2 1 at 2 ? t 2 ? ? 2 s ? 1 2 = 1 2 =? ? =? ? = ? x1 2 at1 ? 1 ? ? 6 s ? 9 and the correct answer is (c). 2 9. The distance an object moving at a uniform speed of v = 8. 5 m s will travel during a time interval of ? t = 1 1 000 s = 1. 0 ? 10 ? 3 s is given by ? x = v ( ? t ) = (8. 5 m s ) (1. 0 ? 10 ? 3 s ) = 8. 5 ? 10 ? 3 m = 8. 5 mm so the only correct answer to this question is choice (d). 10. Once either ball has left the student’s hand, it is a freely falling body with a constant acceleration a = ? g (taking upward as positive). Therefore, choice (e) cannot be true. The initial velocities of the red and blue balls are given by viR = + v0 and viB = ? 0 , respectively. The velocity of either ball when it has a displacement from the launch point of ? y = ? h (where h is the height of the building) is found from v 2 = vi2 + 2a ( ? y ) as follows: 2 vR = ? viR + 2a ( ? y ) R = ? ( + v0 ) 2 + 2 ( ? g ) ( ? h ) = ? 2 v0 + 2 gh http://helpyoustudy. info 20 Chapter 2 and 2 vB = ? viB + 2a ( ? y ) B = ? ( ? v0 ) 2 + 2 ( ? g ) ( ? h ) = ? 2 v0 + 2 gh Note that the negative sign was chosen for the radical in both cases since each ball is moving in the downward direction immediately before it reaches the ground.From this, we see that choice (c) is tr ue. Also, the speeds of the two balls just before hitting the ground are 2 2 2 2 vR = ? v0 + 2 gh = v0 + 2 gh > v0 and vB = ? v0 + 2 gh = v0 + 2 gh > v0 Therefore, vR = vB , so both choices (a) and (b) are false. However, we see that both ? nal speeds exceed the initial speed and choice (d) is true. The correct answer to this question is then (c) and (d). 11. At ground level, the displacement of the rock from its launch point is ? y = ? h , where h is the 2 height of the tower and upward has been chosen as the positive direction.From v 2 = vo + 2a ( ? y ) , the speed of the rock just before hitting the ground is found to be 2 2 v =  ± v0 + 2a ( ? y ) = v0 + 2 ( ? g ) ( ? h ) = (12 m s )2 + 2 ( 9. 8 m s2 ) ( 40. 0 m ) = 30 m s Choice (b) is therefore the correct response to this question. 12. Once the ball has left the thrower’s hand, it is a freely falling body with a constant, non-zero, acceleration of a = ? g . Since the acceleration of the ball is not zero at any point o n its trajectory, choices (a) through (d) are all false and the correct response is (e). ANSWERS TO EVEN NUMBERED CONCEPTUAL QUESTIONS . Yes. The particle may stop at some instant, but still have an acceleration, as when a ball thrown straight up reaches its maximum height. (a) (b) 6. (a) No. They can be used only when the acceleration is constant. Yes. Zero is a constant. In Figure (c), the images are farther apart for each successive time interval. The object is moving toward the right and speeding up. This means that the acceleration is positive in Figure (c). In Figure (a), the ? rst four images show an increasing distance traveled each time interval and therefore a positive acceleration.However, after the fourth image, the spacing is decreasing, showing that the object is now slowing down (or has negative acceleration). In Figure (b), the images are equally spaced, showing that the object moved the same distance in each time interval. Hence, the velocity is constant in Figure ( b). At the maximum height, the ball is momentarily at rest (i. e. , has zero velocity). The acceleration remains constant, with magnitude equal to the free-fall acceleration g and directed downward. Thus, even though the velocity is momentarily zero, it continues to change, and the ball will begin to gain speed in the downward direction.The acceleration of the ball remains constant in magnitude and direction throughout the ball’s free ? ight, from the instant it leaves the hand until the instant just before it strikes the 4. (b) (c) 8. (a) (b) http://helpyoustudy. info Motion in One Dimension 21 ground. The acceleration is directed downward and has a magnitude equal to the freefall acceleration g. 10. (a) Successive images on the ? lm will be separated by a constant distance if the ball has constant velocity. Starting at the right-most image, the images will be getting closer together as one moves toward the left.Starting at the right-most image, the images will be getting fa rther apart as one moves toward the left. As one moves from left to right, the balls will ? rst get farther apart in each successive image, then closer together when the ball begins to slow down. (b) (c) (d) ANSWERS TO EVEN NUMBERED PROBLEMS 2. 4. 6. (a) (a) (a) (d) 8. (a) (d) 10. 12. (a) (a) (d) 14. 16. (a) 2 ? 10 4 mi 10. 04 m s 5. 00 m s ? 3. 33 m s +4. 0 m s 0 2. 3 min L t1 2 L ( t1 + t 2 ) 1. 3 ? 10 2 s (b) 13 m (b) (b) 64 mi ? L t 2 (c) 0 (b) (b) (b) (e) (b) ? x 2 RE = 2. 4 7. 042 m s 1. 25 m s 0 ? 0. 50 m s (c) ? 1. 0 m s (c) ? 2. 50 m s a) The trailing runner’s speed must be greater than that of the leader, and the leader’s distance from the ? nish line must be great enough to give the trailing runner time to make up the de? cient distance. (b) t = d ( v1 ? v2 ) (c) d2 = v2 d ( v1 ? v2 ) 18. (a) Some data points that can be used to plot the graph are as given below: x (m) t (s) (b) (c) 5. 75 1. 00 16. 0 2. 00 35. 3 3. 00 68. 0 4. 00 119 5. 00 192 6. 00 41. 0 m s , 41. 0 m s , 41. 0 m s 17. 0 m s , much smaller than the instantaneous velocity at t = 4. 00 s l http://helpyoustudy. info 22 Chapter 2 20. 22. 24. (a) 20. 0 m s , 5. 00 m s (b) 263 m 0. 91 s (i) (a) (ii) (a) 0 0 (b) (b) 1. 6 m s 2 1. 6 m s 2 500 x (m) (c) (c) 0. 80 m s 2 0 26. The curves intersect at t = 16. 9 s. car police officer 250 0 0 4. 00 8. 00 12. 0 16. 0 20. 0 t (s) 28. 30. a = 2. 74 ? 10 5 m s 2 = ( 2. 79 ? 10 4 ) g (a) (b) (e) 32. (a) (d) 34. 36. 38. 40. (a) (a) (a) (a) (c) 42. 44. 46. 48. 95 m 29. 1 s 1. 79 s v 2 = vi2 + 2a ( ? x ) f 8. 00 s 13. 5 m 22. 5 m 20. 0 s 5. 51 km 107 m v = a1t1 (c) a = ( v 2 ? vi2 ) 2 ( ? x ) f (d) 1. 25 m s 2 (b) 13. 5 m (c) 13. 5 m (b) (b) (b) (b) No, it cannot land safely on the 0. 800 km runway. 20. 8 m s, 41. 6 m s, 20. 8 m s, 38. 7 m s 1. 49 m s 2 ? = 1 a1t12 2 2 ? xtotal = 1 a1t12 + a1t1t 2 + 1 a2 t 2 2 2 (a) Yes. (b) vtop = 3. 69 m s (c) ?v downward = 2. 39 m s (d) No, ? v upward = 3. 71 m s. The two rocks have the same acceleratio n, but the rock thrown downward has a higher average speed between the two levels, and is accelerated over a smaller time interval. http://helpyoustudy. info Motion in One Dimension 23 50. 52. (a) (a) (c) 21. 1 m s v = ? v0 ? gt = v0 + gt v = v0 ? gt , d = 1 gt 2 2 29. 4 m s ? 202 m s 2 4. 53 s vi = h t + gt 2 (b) (b) 19. 6 m d = 1 gt 2 2 (c) 18. 1 m s, 19. 6 m 54. 56. 58. 60. 62. 64. (a) (a) (a) (a) (b) (b) (b) (b) 44. 1 m 198 m 14. m s v = h t ? gt 2 See Solutions Section for Motion Diagrams. Yes. The minimum acceleration needed to complete the 1 mile distance in the allotted time is amin = 0. 032 m s 2 , considerably less than what she is capable of producing. (a) (c) y1 = h ? v0 t ? 1 gt 2 , y2 = h + v0 t ? 1 gt 2 2 2 2 v1 f = v2 f = ? v0 + 2 gh (d) 66. (b) t 2 ? t1 = 2 v0 g y2 ? y1 = 2 v0 t as long as both balls are still in the air. 68. 70. 3. 10 m s (a) (c) 3. 00 s (b) v0 ,2 = ? 15. 2 m s v1 = ? 31. 4 m s, v2 = ? 34. 8 m s 2. 2 s only if acceleration = 0 (b) (b) ? 21 m s Yes, for all initial velocities and accelerations. 72. 74. (a) (a)PROBLEM SOLUTIONS 2. 1 We assume that you are approximately 2 m tall and that the nerve impulse travels at uniform speed. The elapsed time is then ? t = 2. 2 (a) 2m ? x = = 2 ? 10 ? 2 s = 0. 02 s v 100 m s At constant speed, c = 3 ? 108 m s, the distance light travels in 0. 1 s is ? x = c ( ? t ) = ( 3 ? 108 m s ) ( 0. 1 s ) ? 1 mi ? ? 1 km ? 4 = ( 3 ? 10 7 m ) ? ? = 2 ? 10 mi 3 ? 1. 609 km ? ? 10 m ? (b) Comparing the result of part (a) to the diameter of the Earth, DE, we ? nd 3. 0 ? 10 7 m ? x ? x = = ? 2. 4 DE 2 RE 2 ( 6. 38 ? 10 6 m ) ( with RE = Earth’s radius ) http://helpyoustudy. info 24 Chapter 2 2. 3Distances traveled between pairs of cities are ? x1 = v1 ( ? t1 ) = (80. 0 km h ) ( 0. 500 h ) = 40. 0 km ? x2 = v2 ( ? t 2 ) = (100 km h ) ( 0. 200 h ) = 20. 0 km ? x3 = v3 ( ? t3 ) = ( 40. 0 km h ) ( 0. 750 h ) = 30. 0 km Thus, the total distance traveled is ? x = ( 40. 0 + 20. 0 + 30. 0 ) km = 90. 0 km, a nd the elapsed time is ? t = 0. 500 h + 0. 200 h + 0. 750 h + 0. 250 h = 1. 70 h. (a) (b) v= ? x 90. 0 km = = 52. 9 km h ? t 1. 70 h ?x = 90. 0 km (see above) v= v= ? x 2. 000 ? 10 2 m = = 10. 04 m s ? t 19. 92 s 2. 4 (a) (b) 2. 5 (a) ?x 1. 000 mi ? 1. 609 km ? ? 10 3 m ? = ? ? = 7. 042 m s ? t 228. 5 s ? 1 mi ? 1 km ? Boat A requires 1. 0 h to cross the lake and 1. 0 h to return, total time 2. 0 h. Boat B requires 2. 0 h to cross the lake at which time the race is over. Boat A wins, being 60 km ahead of B when the race ends. Average velocity is the net displacement of the boat divided by the total elapsed time. The winning boat is back where it started, its displacement thus being zero, yielding an average velocity of zero . (b) 2. 6 The average velocity over any time interval is ? x x f ? xi = ? t t f ? ti ? x 10. 0 m ? 0 v= = = 5. 00 m s ? t 2. 00 s ? 0 v= (a) (b) (c) (d) (e) v= v= v= v= ? x 5. 00 m ? 0 = = 1. 25 m s ? 4. 00 s ? 0 ? x 5. 00 m ? 10. 0 m = = ? 2. 50 m s ? t 4. 00 s ? 2. 00 s ? x ? 5. 00 m ? 5. 00 m = = ? 3. 33 m s ? t 7. 00 s ? 4. 00 s 0? 0 ? x x2 ? x1 = = = 0 ? t t 2 ? t1 8. 00 s ? 0 2. 7 (a) (b) 1h ? Displacement = ? x = (85. 0 km h ) ( 35. 0 min ) ? ? ? + 130 km = 180 km ? 60. 0 min ? 1h ? The total elapsed time is ? t = ( 35. 0 min + 15. 0 min ) ? ? ? + 2. 00 h = 2. 83 h ? 60. 0 min ? so, v= ? x 180 km = = 63. 6 km h ? t 2. 84 h http://helpyoustudy. info Motion in One Dimension 25 2. 8 The average velocity over any time interval is ? x x f ? xi = ? t t f ? ti ? x 4. 0 m ? 0 v= = = + 4. 0 m s ? t 1. 0 s ? 0 ? ? 2 . 0 m ? 0 v= = = ? 0. 50 m s ? t 4. 0 s ? 0 v= (a) (b) (c) (d) v= v= ? x 0 ? 4. 0 m = = ? 1. 0 m s ? t 5. 0 s ? 1. 0 s ? x 0? 0 = = 0 ? t 5. 0 s ? 0 2. 9 The plane starts from rest ( v0 = 0 ) and maintains a constant acceleration of a = +1. 3 m s 2 . Thus, we ? nd the distance it will travel before reaching the required takeoff speed ( v = 75 m s ) , from 2 v 2 = v0 + 2a ( ? x ) , as ? x = 2 v 2 ? v0 ( 75 m s ) ? 0 = = 2. 2 ? 10 3 m = 2. 2 km 2 2a 2 (1. 3 m s ) 2 Since this distance is less than the length of the runway, the plane takes off safely. 2. 10 (a) The time for a car to make the trip is t = cars to omplete the same 10 mile trip is ? t = t1 ? t 2 = (b) ? x ? x ? 10 mi 10 mi ? ? 60 min ? ? =? ? ? = 2. 3 min v1 v2 ? 55 mi h 70 mi h ? ? 1 h ? ?x . Thus, the difference in the times for the two v When the faster car has a 15. 0 min lead, it is ahead by a distance equal to that traveled by the slower car in a time of 15. 0 min. This distance is given by ? x1 = v1 ( ? t ) = ( 55 mi h ) (15 min ). The faster car pulls ahead of the slower car at a rate of vrelative = 70 mi h ? 55 mi h = 15 mi h Thus, the time required for it to get distance ? x1 ahead is ? t = ? x1 = vrelative ( 55 mi h ) (15 min ) 15. 0 mi h = 55 minFinally, the distance the faster car has traveled during this time is ? x2 = v2 ( ? t ) = 2. 11 (a) ( 70 mi h ) ( 55 min ) ? ? 1h ? ? = 64 mi ? 60 min ? From v 2 = vi2 + 2a ( ? x ) , with vi = 0 , v f = 72 km h , and ? x = 45 m, the acceleration of the f cheetah is found to be km ? ? 10 3 m ? ? 1 h 72 ? 0 h ? ? 1 km ? ? 3 600 s v 2 ? vi2 f a= = = 4. 4 m s 2 2 ( ? x ) 2 ( 45 m ) continued on next page 2 http://helpyoustudy. info 26 Chapter 2 (b) The cheetah’s displacement 3. 5 s after starting from rest is 1 1 2 ? x = vi t + at 2 = 0 + ( 4. 4 m s 2 ) ( 3. 5 s ) = 27 m 2 2 2. 12 (a) (b) (c) (d) 1 = v2 = ( ? x )1 + L = = + L t1 ( ? t )1 t1 ( ? x )2 ? L = = ? L t2 ( ? t )2 t 2 ( ? x ) total ( ? x )1 + ( ? x )2 + L ? L 0 = = = 0 = t1 + t 2 t1 + t 2 t1 + t 2 ( ? t ) total +L + ? L total distance traveled ( ? x )1 + ( ? x )2 2L = = = ( ave. speed )trip = t1 + t 2 t1 + t 2 t1 + t 2 ( ? t ) total vtotal = The total time for the trip is t total = t1 + 22 . 0 min = t1 + 0. 367 h , where t1 is the time spent traveling at v1 = 89. 5 km h. Thus, the distance traveled is ? x = v1 t1 = vt total, which gives 2. 13 (a) (89. 5 km h ) t1 = ( 77. 8 km h ) ( t1 + 0. 367 h ) = ( 77. 8 km h ) t1 + 28. 5 km or, (89. 5 km h ? 77. km h ) t1 = 28. 5 km From which, t1 = 2 . 44 h for a total time of t total = t1 + 0. 367 h = 2. 81 h (b) The distance traveled during the trip is ? x = v1 t1 = vt total, giving ? x = v ttotal = ( 77. 8 km h ) ( 2. 81 h ) = 219 km 2. 14 (a) At the end of the race, the tortoise has been moving for time t and the hare for a time t ? 2 . 0 min = t ? 120 s. The speed of the tortoise is vt = 0. 100 m s, and the speed of the hare is vh = 20 vt = 2 . 0 m s. The tortoise travels distance xt, which is 0. 20 m larger than the distance xh traveled by the hare. Hence, xt = xh + 0. 20 m which becomes or vt t = vh ( t ? 120 s ) + 0. 0 m ( 0. 100 m s ) t = ( 2 . 0 m s ) ( t ? 120 s ) + 0. 20 m t = 1. 3 ? 10 2 s This gives the time of the race as (b) 2. 15 xt = vt t = ( 0. 100 m s ) (1. 3 ? 10 2 s ) = 13 m The maximum allowed time to complete the trip is t total = total distance 1600 m ? 1 km h ? = ? ? = 23. 0 s required average speed 250 km h ? 0. 2 78 m s ? The time spent in the ? rst half of the trip is t1 = half distance 800 m ? 1 km h ? = ? ? = 12 . 5 s v1 230 km h ? 0. 278 m s ? continued on next page http://helpyoustudy. info Motion in One Dimension 27 Thus, the maximum time that can be spent on the second half of the trip is t 2 = t total ? 1 = 23. 0 s ? 12 . 5 s = 10. 5 s and the required average speed on the second half is v2 = 2. 16 (a) ? 1 km h ? half distance 800 m = = 76. 2 m s ? ? = 274 km h t2 10. 5 s ? 0. 278 m s ? In order for the trailing athlete to be able to catch the leader, his speed (v1) must be greater than that of the leading athlete (v2), and the distance between the leading athlete and the ? nish line must be great enough to give the trailing athlete suf? cient time to make up the de? cient distance, d. During a time t the leading athlete will travel a distance d2 = v2 t and the trailing athlete will travel a distance d1 = v1t .Only when d1 = d2 + d (where d is the initial distance the trailing athlet e was behind the leader) will the trailing athlete have caught the leader. Requiring that this condition be satis? ed gives the elapsed time required for the second athlete to overtake the ? rst: d1 = d2 + d giving or v1t = v2 t + d or t = d ( v1 ? v2 ) (b) v1t ? v2 t = d (c) In order for the trailing athlete to be able to at least tie for ? rst place, the initial distance D between the leader and the ? nish line must be greater than or equal to the distance the leader can travel in the time t calculated above (i. e. , the time required to overtake the leader).That is, we must require that D ? d2 = v2 t = v2 ? d ( v1 ? v2 ) ? ? ? or D? v2 d v1 ? v2 2. 17 The instantaneous velocity at any time is the slope of the x vs. t graph at that time. We compute this slope by using two points on a straight segment of the curve, one point on each side of the point of interest. (a) (b) (c) (d) vt=1. 00 s = vt=3. 00 s = 10. 0 m ? 0 = 5. 00 m s 2 . 00 s ? 0 ( 5. 00 ? 10. 0 ) m = ? 2 . 50 m s ( 4. 0 0 ? 2 . 00 ) s ( 5. 00 ? 5. 00 ) m vt=4. 50 s = = 0 ( 5. 00 ? 4. 00 ) s 0 ? ( ? 5. 00 m ) vt=7. 50 s = = 5. 00 m s (8. 00 ? 7. 00 ) s http://helpyoustudy. info 28 Chapter 2 2. 18