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?大学物理?英文课件4MotioninTwoandThreeDimensionsPositionandDisplacementPositionvectorRectangularcoordinates

SampleProblemProblem:Arabbitrunsacrossaparkinglotonwhichasetofcoordinateaxeshas,strangelyenough,beendrawn.Thecoordinates(meters)oftherabbit’spositionasfunctionsoftimet(seconds)aregivenbyxt2t+28,yt2t+30.findthevelocityattimet=15s.Solution:AverageandInstantaneousAcceleration

instantaneousacceleration:

SampleProblemProblem:Arabbitrunsacrossaparkinglotonwhichasetofcoordinateaxeshas,strangelyenough,beendrawn.Thecoordinates(meters)oftherabbit’spositionasfunctionsoftimet(seconds)aregivenbyxt2t+28,yt2t+30.findthevelocityattimet=15s.Solution:Features:thehorizontalmotionandtheverticalmotionareindependentofeachother

ProjectileMotionProjectileMotionAnalyzed

HorizontalMotion:velocityremainsconstantTheVerticalMotion:asfree-fallmotionTheEquationofPathProjectileMotionAnalyzed

TheHorizontalRange

SampleProblemProblem:IntheFigure,arescueplanefliesat198km/h(=55.0m/s)andconstantheighth=500mtowardapointdirectlyoveravictim,wherearescuecapsuleistoland.(a)Whatshouldbetheangleϕofthepilot’slineofsighttothevictimwhenthecapsulereleaseismade?(b)Asthecapsulereachesthewater,whatisitsvelocityinunit-vectornotationandinmagnitude-anglenotation?Solution:(a)SampleProblem

(b)SampleProblemProblem:Thefigureshowsapirateship560mfromafortdefendingaharborentrance.Adefensecannon,locatedatsealevel,firesballsatinitialspeedv0=82m/s.(a)Atwhatangleθ0fromthehorizontalmustaballbefiredtohittheship?(b)Whatisthemaximumrangeofthecannonballs?Solution:(a)(b)Evenconstantspeed,thevelocitychangesindirection.Thevelocityisalwaysdirectedtangenttothecircleinthedirectionofmotion.UniformCircularMotionTheaccelerationisalwaysdirectedradiallyinward.CentripetalaccelerationvelocitydependsonthereferenceframeFrameAonthegroundFrameBonmovingcarObjectPonanothercarRelativeMotioninOneDimensionSampleProblemProblem:Inthefigure,supposethatBarbara’svelocityrelativetoAlexisaconstantvBA=52km/handcarPismovinginthenegativedirectionofthexaxis.(a)IfAlexmeasuresaconstantvPA=-78km/hforcarP,whatvelocityvPBwillBarbarameasure?(b)IfcarPbrakestoastoprelativetoAlex(andthusrelativetotheground)intimet=10satconstantacceleration,whatisitsaccelerationaPArelativetoAlex?(c)WhatistheaccelerationaPBofcarPrelativetoBarbaraduringthebraking?Solution:(a)SampleProblem(b)(c)RelativeMotioninTwoDimensions

SampleProblemProblem:Inthefigure,aplanemovesdueeastwhilethepilotpointstheplanesomewhatsouthofeast,towardasteadywindthatblowstothenortheast.TheplanehasvelocityvPWrelativetothewind,withanairspeed(speedrelativetothewind)of215km/h,directedatangleθsouthofeast.ThewindhasvelocityvWGrelativetothegroundwithspeed65.0km/h,direct

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