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1、4KINEMATICSINTWODIMENSIONSConceptualQuestionsd4.1.(a)Asshowninthefigurebelow,theaccelerationacanbedividedintocomponentsperpendicular()⊥anddparallel()
2、
3、tothevelocity.a
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5、willslowtheparticledownsinceitisintheoppositedirectiontov.d(b)Theperpendicularcomponentofaa,,⊥ispointingtothe
6、right,andchangestheparticledirectiontotheright.4.2.(a)Acomponentoftheaccelerationeitherparallelorantiparalleltothevelocitywouldspeeduptheparticleorslowitdown,respectively.Sincethereisnoparallelcomponentthenthespeedisn’tchanging.d(b)Theperpendicularcomponentofaa,,⊥ispointingdow
7、n,andchangestheparticledirectioninthatdirection.4.3.ApproximateTarzanasaparticleinnonuniformcircularmotion.d(a)AsTarzanjuststepsoffthevine,hisvelocityiszero,butincreasingalonghistrajectory,soaisalongthe2dvtrajectory.Thecomponentofathatisthecentripetalaccelerationar==0becausev=
8、0.r2dvvttd(b)Atthebottomoftheswing,ar=≠0,butthevelocityisatamaximum,soat==0,soaisnotzerordtandpointsup.4.4.Atypicaltrajectoryofaprojectileisshowninthefigurebelow.Theaccelerationduetogravityalwayspointsdown.Thevelocitychangesdirectionfromthelaunchangleθθ=0abovethe+x-axistozeroa
9、tthetopofthetrajectory,toθθ=0belowthe+x-axiswhenithitstheground.ddv1y(a)Atnotimearevandaparallelif=°tan30v1xdd(b)Atthetopofthetrajectoryvandaareperpendicular.©Copyright2013PearsonEducation,Inc.Allrightsreserved.Thismaterialisprotectedunderallcopyrightlawsastheycurrentlyexist.N
10、oportionofthismaterialmaybereproduced,inanyformorbyanymeans,withoutpermissioninwritingfromthepublisher.4-14-2Chapter44.5.Foraprojectile,only,,vaxxandayareconstantduringtheflight.Sincetheaccelerationagy=−isdown,a=0andvisconstant.Thenonzeroaisconstantlychangingv,sothetotalspeedv
11、vv=+22changesasxxyyxywell.Thepositionsxandychange,sorxy=+22changes,too.Onlyaiszerothroughouttheflight.x4.6.(a)Theballfiredupwardisaprojectilewithahorizontalcomponentofinitialvelocityequaltothecart’sspeed.Withoutairfriction,thereisnohorizontalcomponentoftheacceleration,sothebal
12、lstaysoverthecartduringthewholeflight,andlandsdirectlybackint
