chapter 1 linear motion example problems - doc fizzix ... · pdf filethe fastest man alive can...

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Example Problems

1.1 Speed• Example1:(HowFast)-Anelephantrunningattopspeedcantravel26.84metersin4seconds,whatistheelephant’saveragespeedinmeterspersecond?

Write the formula and show your workWhat are the givens and unknowns?

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• Example2:(HowFast)-Thefastestofallthedogbreedsisagreyhound.Agreyhoundcanrun120.72metersin6seconds,whatisthegreyhound’saveragespeedinm/s?


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• Example3:(HowFar)-Amonkeyridingabiketravelsataconstantspeedof4.3m/sfor5s.Howfardoesthatmonkeytravel?


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Doc Fizzix ExampleProblems•Speed

Chapter 1 Linear Motion

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• Example4:(HowFar)-Amonkey,inhisPorscheistravelingat20m/swhenheseesagorillastandinginthemiddleoftheroad.Ittakesthemonkey0.8storeactbeforeapplyingthebrakes.Howfardoesthemonkeytravelbeforethebrakesareapplied?


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• Example5:(HowLong)-YouaredrivingfromAustin,TXtoSt.Paul,MNatanaveragespeedof35.76m/s(80mph).ThetotaltraveldistancefromAustinis1,905,463meters(1,184miles).How longwill it take you to reach your destination? Convert your answer tominuetsandthenhours.


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• Example6:(HowLong)-Theaveragepersonwalksatarateof1.4m/s(3.1mph).ThecircumferenceoftheEarthattheequatoris40,075,884meters(24,902miles).HowlongwouldittakeapersontowalkaroundtheEarth?Convertyouranswertominuets,thenhours,andthendays.Note:1hourisequalto3,600seconds.


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Doc Fizzix ExampleProblems•Speed


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Student Problems

1.1 SpeedYOU MUST SHOW ALL WORK! (Formulas, plug in numbers, answer boxed, units)

1. The fastestman alive can run the 100-meter dash in 9.58 seconds, calculate theaveragespeedinmeterspersecond.

Substitute the known values and solve.

Write the formula you are usingWhat are the givens and unknowns?

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2. Thefastestlandanimalisthecheetah.Acheetahcanrunthe100-meterdashin5.95seconds,calculatethecheetah’saveragespeedinmeterspersecond.



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Doc Fizzix StudentProblems•Speed


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3. Therecordtimefortheonemilerunis3minand43sec,calculatetheaveragespeedinmeterspersecond.(Onemileisequalto1,609.34meters)



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4. Amonkeywalksatapaceof1.5m/sfor25seconds,howfardoeshetravel?



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5. Youare speedingdown thehighway at a rate of 33.53m/s (75mph)whenyousuddenlyseeapolicespeedtrapsoyouquicklytrytoslowdowninordertogetbellowyourcurrentspeed.Ifittakesyou0.89secondstoreacttowhatyouseeandapplythebrakes,howfardoyoutravelduringyourreactiontime?



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6. Amonkeywatchesathunderstormfromhisbackporch.Heseesaflashoflightningoffinthedistanceandbeginscountingthesecondsuntilhehearstheclapofthunder5secondslater.Assumethatthespeedofsoundinairis340m/s,howfarawaywasthelightningboltinmeters?



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7. Anecho iscausedwhenasoundwave travelsawayfromasource,hitsa target,andthenbouncingback.Soundtravelsataspeedof340m/sinair. Ifyoustandat the rimof theGrandCanyon andyell down towards the bottom, itwill take5.20secondsforthesoundtotraveltothecanyonfloorandthenback.Whatisthetotaldistancethesoundwavetravels(thereandback)andhowdeepistheGrandCanyonatthislocation?



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8. Atopprofessionalbaseballpitchercanthrowabaseballataspeedof44.70m/s(100mph).Thedistance fromthepitchersmoundto thecatcher is18.39meters.Howmuchtimedoesthebatterhavetoreacttoapitchthrownat44.70m/s?



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9. Antscanrunatanaveragespeedof0.083meterspersecond,howlongwouldittakeananttorunthe100-meterdashinseconds?Howmanyminuetswouldthistake?



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10. Themoonisanaveragedistanceof382,500,000meters(238,855miles)fromtheEarth.Ifyouwereabletodriveacaratanaveragespeedof44.70m/s(100mph)allthewaytothemoonhowlongwouldittakeyoutoreachyourdestinationinseconds?Converttominuets,hours,anddays?Note:1hourisequalto3,600seconds.



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Doc Fizzix ExampleProblems•DistanceandDisplacement


Example Problems

1.2 Distance and Displacement• Example1:-Agirlleavesherhistoryclassroomandwalks10metersnorthtoadrinkingfountain.Thensheturnsandwalks30meterssouthtoherartclassroom.Whatisthegirl’stotaldisplacementfromherhistoryclassroomandwhatisthetotaldistanceshetraveled?

• Example2:-Abirdflieswestfor8.5kilometersandeastfor3kilometers,andthenturnsaroundandheadsbackwestfor2kilometers.Whatisthetotaldistancethebirdtravelsandwhatisthebirdsdisplacement?

• Example3:-Inadrillduringbasketballpractice,aplayerrunsthelengthofthe30metercourtandback.Theplayerdoesthisthreetimesin60seconds.Whatisthemagnitudeoftheplayer’stotaldisplacementandwhatisthetotaldistancetraveled?

• Example4:-Apersontravels23metersnorthin16sec,5meterssouthin4sec,and16metersnorthin18sec.Whatwasthetotaldistancetraveledandwhatisthetotaldisplacement?

• Example5:-Fromtheproblemabovewhatistheperson’saveragespeedandaveragevelocity?

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Doc Fizzix ExampleProblems•DistanceandDisplacement


• Example6:-Amonkeytravels48.28mnorthin12sec,then40msouthin27sec.Whatisthemonkey’saveragespeedandtheaveragevelocityinm/s?

• Example7:-Onahighway,acarisdriven80kilometersduringthefirst1.00houroftravel,50kilometersduringthenext0.50hours,and40kilometersinthefinal0.50hours.Whatisthecar’saveragespeedfortheentiretripinkm/hr?

• Example8:-Acartravels90metersduenorthin15seconds.Thenthecarturnsaroundandtravels 40metersdue south in 5.0 seconds.What is themagnitudeof the car’saveragevelocityfortheentiretrip?

• Example9:-Aballshotintotheairtravelstoamaximumheightof20metersandthenfallsbacktothereleasepointin4seconds.Whatwastheaveragespeedoftheballandwhatistheaveragevelocityoftheballinmeterspersecond?

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Example Problems

1.3 Acceleration• Example1:-TheLamborghiniMurcielagocanacceleratefrom0to27.8m/s(62.2mph)inatimeof3.40seconds.Determinethemagnitudeoftheacceleration.


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• Example2:-AnIndy500racecar’svelocityincreasesfrom4.0m/sto36m/sina4.0-stimeinterval.Whatistheracercar’saverageacceleration?


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• Example3:-ThedriverofaFerrariFormulaOnecarapplies fullbrakesslowingthevehiclefrom27.8m/sto0in1.22seconds.Determinethemagnitudeanddirectionoftheaccelerationunderfullbraking.


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Doc Fizzix ExampleProblems•Acceleration


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• Example4:-Amonkeyistravelingat8.33m/swhenheacceleratesataconstantrateof3.5m/s².Whatisthevelocityofthemonkeyaftervelocity7.3seconds?


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• Example5:-Amonkeyisplayingminiaturegolf.Themonkeyhitsthegolfballandtheballrollsupahilltowardthehole.Iftheballstartswithaspeedof2.0m/sandslowsataconstantrateof-0.32m/s²,whatistheballsfinalvelocityafter2.0s?


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• Example6:-Ifacaracceleratesfromrestataconstant5.5m/s²,howlongwillittaketoreachavelocityof28m/s?


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• Example7:-Acaritslowedfrom22m/sto3.0m/sataconstantrateof2.1m/s².Howlongwillittakebeforethecaristravelingatafinalvelocityof3.0m/s?


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• Example8:-Acardrivenbyamonkeyhasstalledandisrollingbackwardsdownhillwithaspeed of 3.0m/s. Themonkey suddenly get the car started again and beginsaccelerating up the hill.After 2.5 s, the car ismoving uphill at a speed of 4.5m/s.Assumingthattheuphilldirectionisthepositive,whatisthecar’saverageaccelerationduringthisentireevent?


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Student Problems

1.3 AccelerationYOU MUST SHOW ALL WORK! (Formulas, plug in numbers, answer boxed, units)

11. The“average”carontheroadwillgofrom0to27m/s(0-60mph)in7.71seconds.Calculatethemagnitudeoftheaccelerationforthe“average”carinm/s²?


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12. Thehighest launchaccelerationof a roller coaster is in Japan.TheDodonpa canchangevelocityfrom0-47.83m/s(0-107mph)in1.8secondspulling2.7g’s,whatisthemagnitudeoftheDodonparollercoaster’saccelerationoftheinm/s²?


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Doc Fizzix StudentProblems•Acceleration


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13. TheBatmobileisinitiallytravelingat8.3m/swhenitspeedsuptoafinalvelocityof32.1m/sin6.8s,whatisthemagnitudeoftheBatmobile’sacceleration?


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14. Amonkey is ridinghisbike travelingwithan initialvelocityof9.6m/swhenhestartspeddlingfasterandfasteracceleratingtoafinalvelocityof19.5m/s in4.5seconds.Whatisthemagnitudeofthemonkey’sacceleration?


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15. Acar,drivenbyamonkey,istravelingatavelocityof24.59m/swhenthemonkeyseesagorillacrossingtheroadupaheadandhastoslamsonthebrakes.Ifittakesthecar4.2secondstocometorestwhatisthemagnitudeofthecar’sacceleration?


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16. Amonkeyisdrivingacarat26.82m/swhenhetakeshisfootoffthegasandcoastfor4.5seconds;thiscausesthevehicletoslowdowntoafinalvelocityof18.7m/s.Whatisthemagnitudeofthevehicle’sacceleration?


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17. Onadryroadacarwithgoodtirescandecelerateat4.92m/s².Howlongwouldittakeacarinitiallytravelingat24.6m/stocometorest?


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18. Theheadofarattlesnakecanaccelerateatamagnitudeof50m/s²asitstrikesit’svictim.Ifacarcouldhavethesameaccelerationasarattlesnake,howmuchtimewouldittakeforthecartogofrom0m/sto26.82m/s(0-60mph)?


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19. Thebrakesonthe“average”automobilearecapableofslowingacaratarateof5.18m/s².Ifyouaretravelingat80mph(35.76m/s)whenyousuddenlyseeastatetrooperonthehighway,howmuchtimewillittakeyoutoslowyourcardowntothespeedlimitifthepostedspeedis65mph(29.06m/s)?


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Example Problems

1.4 Kinematics• Example1:-Supermanisflyingat145m/swhenhesuddenlyincreaseshisspeeduniformlyatarateof23.1m/s²for20.0s.WhatisSuperman’sfinalvelocity?

Write the formula and show your work

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• Example2:-TheFlashhasaninitialvelocityof22m/swhenheincreaseshisspeeduniformlyattherateof1.6m/s²for6.8s.WhatisTheFlash’sfinalvelocity?


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• Example3:-HowfardoesSupermanflyin15swhilehechangeshisvelocityfrom145m/sto75m/satauniformrateofacceleration?


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Doc Fizzix ExampleProblems•Kinematics


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• Example4:-Acartravelingonastraightroadat15.0m/sthenacceleratesuniformlytoaspeedof21.0m/sfor12.0seconds.Whatisthetotaldistancethecartravelsin12.0seconds?


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• Example5:-Anairplanestartsfromrestandacceleratesataconstant3.00m/s²for30.0sbeforeleavingtheground.Whatistheplane’sdisplacementbeforeitleavetheground?


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• Example6:- A monkey is jogging with an initial velocity of 4.2 m/s when he acceleratesuniformlyatarateof4.1m/s²for7secondsalongastraightlinepath.Whatisthemagnitudeofthemonkey’sdisplacement?


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• Example7:-Supermanstartsfromrestandacceleratesuniformlyatarateof5.0m/s².WhatisSuperman’sfinalvelocityafterhehastraveled500meters?


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• Example8:-Aracecarcanbeslowedwithaconstantaccelerationof–11m/s².Ifthecarisgoing55m/s,howmanymeterswillittakethecartocometoatostop?


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Doc Fizzix WxampleProblems•Kinematics


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Student Problems

1.4 KinematicsYOU MUST SHOW ALL WORK! (Formulas, plug in numbers, answer boxed, units)

20. Amonkey on a skateboard starts from rest at the top of a big hill. Themonkeypushesoffandheadsdownthehillacceleratingatarateof2.3m/s²for15s.Whatisthemonkey’sfinalvelocityafter15seconds?



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21. SquidwardTentaclesistravelingthroughaschoolzonewithavelocityof13.41m/s(30mph).AttheendoftheschoolzoneSquidwardacceleratesatarateof5m/s²inordertogetbackuptospeed,whatisSquidward’svelocityafter2.5seconds.



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Doc Fizzix StudentProblems•Kinematics


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22. ASandyCheeksiscoastingonherskateboardwithaninitialvelocityof4m/swhenshecomestothebottomofahillandbeginstoslowdeceleratinguniformlyattherateof1.6m/s²for2.7s.WhatistheSandy’sfinalvelocityattheendofthe2.7s?



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23. ASpong-Bobisstartingfromrestonhisscooterandacceleratesuniformlyatarateof4.90m/s².WhatisSpong-Bob’svelocityafterhehastraveled200-meters?



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24. PatrickStarisinitiallyjoggingwithaninitialvelocityof5.0m/swhenheacceleratesuniformlyat2.3m/s²for12secondsalongastraightlinepath.WhatisthemagnitudeofthePatrick’sdisplacementduringthis12-secondinterval?



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25. HowfardoesMr.Crabtravelin15sashechangeshisvelocityfrom24.58m/s(55mph)to31.29m/s(70mph)atauniformrateofacceleration?



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26. Whatisthedistancecoveredbyaformula1racecarthatstartsfromrestacceleratingat11.18m/s²toafinalvelocityof44.70m/s(0-100mph)?



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27. Atopfueldragstercanaccelerateatarateof44m/s².Howfastwillthedragsterbemovingifitstartsfromrestandacceleratesuniformlyallthewaytothefinish402metersaway(quarter-mile)?



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28. RickeyHenderson,baseball’srecordholderforstolenbases,approachesthirdbase.Hedivesheadfirst,hittingthegroundat6.75m/sandreachingthebaseat5.91m/s,acceleratingat-5.11m/s/s.DeterminethedistanceRickeyslidesacrossthegroundbeforetouchingthebase.



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29. A 2015 Porsche BoxsterGTS can go from 0m/s to 26.82m/s (0-60mph) in 4.2seconds.Assumingtheaccelerationremainsconstant(intherealworlditdoesnot),whatistheaccelerationoftheBoxsterandhowfardoesittravel?



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Example Problems

1.5 Free Fall• Example1:-Amonkeydropsabrickfromascaffoldwhiledoingsomestoneworkonaverytallbuilding.Whatisthevelocityofthebrickafter4.0sandhowfardoesitfall?


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• Example2:-Acoconutisdroppedfromahoveringhelicopterbyamonkeytryingtohitagorillaontheheadbellow.Afterit’srelease,whatisthevelocityofthecoconutandhowfardoeshasitfallenafter6seconds?


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• Example3:-Inordertoopenaclamaseagullhaslearnedtodroptheclamontoahardsurfacefromhighpoint.Ifaseagullfliestoaheightof25manddropstheclam,howlongwilltheclambeintheairandhowfastwillitbemovingwhenithitstheground?


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Doc Fizzix ExampleProblems•FreeFall


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• Example4:-According toGuinness, the tallestman tohaveever livedwasRobertPershingWadlowofAlton,Illinois.Hewaslastmeasuredin1940tobe2.72meterstall(8feet,11inches).Determinehowlongitwouldtakeaquartertohitthegroundandhowfastitwillbemovingifdroppedfromthetopofhishead.


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• Example5:-AtSixFlagsoverTexas,apopularrideknownas“TheScream”carriespassengersup toaheightof 62.5mand thendrops them to theground.How fast are thepassengersgoingatthebottomoftherideandhowlongdoesthefalltake?


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• Example6:-Astoneisthrownverticallydownfromtheroofofabuildingbyamonkey.Thestonepassesawindow14.0mbellowtheroofwithaspeedof22.0m/sandhitstheground2.80safteritwasinitialthrown.Determinetheinitialvelocityofthestoneandtheheightofthebuilding.


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• Example7:-Amonkeyissittingupinatreewhenhelooksdownandseesagorillastandingbeneathhimontheground.Themonkeytakesaimandthenthrowsthecoconutatthegorilla.Ifthecoconutleavethemonkey’shandtravelingat5m/sandthegorillaislocated10metersbelowthemonkey,howlongdoesittakethecoconuttohitthegorillaandhowfastisittravelingwhenitlandsonthegorillashead?


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• Example8:-AnastronautstandingonaplatformonMarsdropsahammer.Ifthehammerfallsadistanceof6.0metersin1.78seconds,whatisitsaccelerationofgravityontheMars?


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• Example9:-AnastronautstandingonaplatformonJupiterdropsahammer.Ifthehammerfallsadistanceof6.0metersin0.68seconds,whatisitsaccelerationofgravityontheJupiter?


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Student Problems

1.5 Free FallYOU MUST SHOW ALL WORK! (Formulas, plug in numbers, answer boxed, units)

30. Amonkeyisstandingunderacoconuttreewhenacoconutfallsfromthetreeandhitsthemonkeyonhishead.Ifthetimeoffallwas1.8s,howfastwasthenutfallingwhenithitthemonkeyontheheadandhowfardidthecoconutfall?



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31. Abaseballdroppedfromthetopofabuildingtakes3.1secondstohittheground.Howfastistheballtravelingwhenithitsthegroundandhowtallisthebuilding?



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32. TheaccelerationofgravityonMarsis3.72m/s².Ifaballisdroppedfromresthowandhitsthegroundin4secondshowfardidtheballfallandhowfastisitmovingwhenithitstheground?



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33. TheaccelerationofgravityonJupiteris24.5m/s².Ifaballisdroppedfromresthowandhitsthegroundin4secondshowfardidtheballfallandhowfastisitmovingwhenithitstheground?



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34. YouareontheobservationdeckoftheUTTowerattheUniversityofTexascampus.Youwanttogetaroughestimateofhowhighupyouaresoyoudropaquarterfromtheobservationdeckandcounthowmanysecondsittakesbeforeforthequartertohittheground.Yourroughcountgivesyouatimeof4seconds.Howhighupareyouandwhatisthevelocityofthecoinasithitstheground?



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35. Amonkeywavestothecrowdbellowandthen jumpsfroma120-mhighbridgewithoutfirstattachingthebungeecord.Howlongdoesthemonkeyhavetothinkabouthiserrorandhowfastwillthemonkeybetravelingwhenhehitstheground?



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36. Youdrop a penny from the observation deck located on the 102 ndfloor of theEmpireStatebuildinginNewYorkCity381m(1,250ft)abovetheground.Howlongdoesittakethepennytohitthegroundandhowfastisthepennyfallingwhenitdoeshittheground?



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37. AraindropfallstotheEarthfromacloud1,700mabovetheEarth’ssurface.Iftheraindropwasnotslowedbyairresistancehowlongwillittaketheraindroptohitthegroundandhowfastwilltheraindropbefallingbythetimeithittheground?



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38. Aballisthrowntowardsthegroundfromawindow50mabovethegroundwithaninitialspeedof12.0m/s.Howlongandhowfastwilltheballbetravelingwhenithitstheground?



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39. Amonkeyisstandingontheporchofhistreehouseandthrowsabananawithavelocityof20m/stowardsagorillastandingontheground.Thebananahitsthegorillaontheheadtraveling39.70m/s.Howhighupisthemonkey’streehouse?



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40. AnastronautisstandingonaplatformontheMoonwhenhedropsahammer.Ifthehammerfallsadistanceof6.0metersin2.7seconds,whatisitsaccelerationofgravityonthemoon?



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41. Onaplanetruledbyapes,arockisdroppedfromrestandtakes0.63secondstofallsaverticaldistanceof0.72meter.Whatisthemagnitudeoftheaccelerationduetogravityonthissocalled“PlanetoftheApes”?



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Example Problems

1.6 Going Up• Example1:-Amonkeyistryingouttobeaballerina.Themonkeyperformsapirouettejumpbyjumpingstraightupintheairwithaninitialspeedof1.8m/s.Howlongisthemonkeyintheairandhowhighdoesshego?


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• Example2:-Atennisballisthrownstraightupwithaninitialspeedof22.5m/s.Howlongistheballintheairandhowhighdoesitgo?


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• Example3:- The Steamboat Geyser in Yellowstone National Park, Wyoming, is capable ofshootingitshotwaterupfromthegroundwithaspeedof48.0m/s.Howhighcanthisgeysershoot?


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• Example4:-Duringabaseballgame,abatterhitsahighpop-up.Iftheballremainsintheairfor6.0s,howhighdoesitriseandwhatwastheoriginalvelocityoftheballasitleftthebat?


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• Example5:-Astartledarmadillojumpsstraightupintotheair.Ifthetotaltimethearmadilloisintheairis0.87secondhowhighdiditriseandwhatwastheoriginalvelocityofthejump?


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• Example6:-Withwhatinitialspeedmustaballbethrownupwardtoreachaheightof24.0mandhowlongwilltheballstayintheair?


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• Example7:-FormerNBAplayer,MichaelJordan,hasanimpressiveverticaljumpof1.22meters.WhatwastheoriginalvelocityasMichaelJordanleftthefloorandwhatisthetotalhangtime?


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Student Problems

1.6 Going UpYOU MUST SHOW ALL WORK! (Formulas, plug in numbers, answer boxed, units)

42. Abulletisfiredfromagunpointedstraightupintotheairwithamuzzlevelocityof460m/s.Howlongdoesittakebullettoreachitsmaximumheightandwhatisthemaximumheightattainedbythebullet?



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43. Amonkeyistryingouttobeabaseballplayer.Themonkeytrytoperformadunkandjumpsstraightupintotheairwithaninitialspeedof2.8m/s.Ifthehoopis3.05mfromtheground,doesthemonkeymakethedunkandhowlongisheintheair?



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44. Atthebeginningofabasketballgame,arefereetossestheballstraightupintotheairwithaspeedof4.6m/s.Aplayercannot touch theballuntil theball reachesit’smaximumheight.What is theminimum time that aplayermustwaitbeforetouchingtheballandhowhighdoestheballgofromitpointofreleased?



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45. Abasketballplayerjumpedstraightuptograbarebound.Ifshewasintheairforatotalof0.80second(upanddown),howhighdidshejump?



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46. Abananaisthrownverticallyupwardbyamonkeyandtakes3.5-secondstoreachit’shighestpoint.Whatisthetotaltimethebananaisintheair,whatwastheoriginalvelocityofthebanana,andwhatwasthemaximumheightattainedbythebanana?



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47. Aballisthrownverticallyupwardandisintheairforatotalof4.6seconds(upanddown),howlongdidittaketheballtoreachit’smaximumheight,whatwastheoriginalvelocityoftheball,andwhatwasthemaximumheightattainedbytheball?



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48. Atwhatspeeddoyouhavetothrowaballintotheairinordertoreachamaximumheightof15metersfromthegroundandhowlongwillitbeintheair?



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49. TheworldrecordforaverticaljumpwasachievedbyKevinBania.Kevenjumpedanincredible1.626meters(64inches)fromastandingstartin2013,calculatehowlongkevenwasintheairandhowfastKevenlefttheground.



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50. Theceilinginaphysicsclassroomis2.6metersfromtheceilingtothefloor.Astudentistryingtobouncearubbersupperballoffthefloorsothatthesubberballbouncestowardstheceilingandthen“just”touchestheceilingabove.Atwhatspeedmustthesupperballbounceoffthefloorinorderto“just”touchtheceiling?



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