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Acannonshootsaclowndirectlyupwardwithaspeedof20m/s.Whatheightwilltheclownreach?

Howmuchtimewilltheclownspendintheair?

ProjectileMotion1:HorizontallyLaunchedProjectiles Twodimensionalmotionismotionconfinedtoaplane(xyaxis)

Motioninaplaneisbrokendownintotwomutuallyperpendicularcomponents.

Thecomponentalongthexaxisisreferredtoashorizontalmotionwhilethecomponentalongtheyaxisisreferredtoasverticalmotion

Horizontalmotionisnotaffectedbyanyexternalforces(aslongasweconsideridealcases)

Verticalmotionisinfluencedbygravity

*Massdoesnotmatter*

THEBIGIDEAWhathappensintheverticaldimension

Whathappensinthehorizontaldimension

Whathappensinthexdimension

Whathappensintheydimension

SoWhatstaysthesamebetweenthehorizontalandvertical?

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Solvingprojectilemotionproblems

Thetable:Forallprojectilemotionproblems:

ay=

Vertical(y)motionis

ax=

Horizontal(x)motionis

Forhorizontally(x)launchedprojectiles,theprojectileislaunchedinthe:_____direction

Acannonfiresaprojectilehorizontally(x)at30m/s.

Whatisthehorizontal(x)componentoftheinitialvelocity?

Whatisthevertical(y)componentoftheinitialvelocity?

Forallhorizontally(x)launchedprojectiles,

Horizontal(x)motionhasnoeffectonvertical(y)motion.

Agunisfiredandabulletisdroppedsimultaneously.Whichbullethitsthegroundfirst,thedroppedorfired?

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Foreachpartofeachproblem,determinewhetheryouaresolvingaverticalorhorizontalmotionproblembeforesolving.LabelXorYinthecolumntotheleft.

2.Acannonshootsaprojectilehorizontally(x)at50m/sfromthetopofa70mtallcliff.

a)Howmuchtimedoesittaketheprojectiletoreachtheground?

b)Whatistherange(dx)oftheprojectile?

3.Aballrollstowardtheedgeofatablethatis110centimetershighandlands2.0metersawayfromitsedge.

a)Howmuchtimedoesittaketheballtoreachtheground?

b)Determinethespeedwithwhichtheballrollsoftheedge.

4.Astuntcartravelingtowardtheedgeofacliffat25meterspersecondlands50metersmeasuredhorizontallyfromtheedgeofthecliff.

a)Howmuchtimedoesittakethecartoreachtheground?

b)Determinetheheightofthecliff.

5.Astuntmanjumpsofftheedgeofa45metertallbuildingtoanairmattressthathasbeenplacedonthestreetbelowat15metersfromtheedgeofthebuilding.

a)Howmuchtimedoesittakethestuntmantoreachtheground?

b)Whatminimuminitialvelocitydoesheneedinordertomakeitontotheairmattress?

VisualizingHorizontallyLaunchedProjectiles

Aprojectileislaunchedhorizontallyat5boxespersecond.

Createamotion/dotdiagramalongthetopforthehorizontal.Putanxoneachspot

Createamotion/dotdiagramalongtheleftforthevertical.Putayoneachspot

Marktheintersectionstoseewheretheprojectilewouldbeinxyspace

Thepathortrajectoryoftheprojectileisa:

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Acceleration Velocity

6.AcarinaJamesBondmoviefliesofftheendofacliffwithavelocityof20m/s.Ifthecarisintheairfor10s,findthefollowinginformation:

a.Theheightofthecliff.

b.Therangethecartraveled.

c.Thelocationofthecarafter5secondsinthexandydirection.

7.A1kgballisrolledofftheendofa1mhightablewithavelocityof2m/s.Findthefollowing:

a.Thetimetheballwasintheair.

b.Therangetheballtraveled.

c.TheimpactvelocityinthexandydirectionANDtheresultantvelocity

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IdentifyingVariables:Identifythefollowingvariables(i.e.dxdyvix,ay,etc.)

8.Astudentstandingontheroofofa80meterhigh(A)buildingkicksastoneatahorizontalspeedof4meterspersecond(B).Howmuchtimedoesittakethestonetohittheground?

Whatisthequestionaskingfor?

Whatarethehiddenorunstatedvariables?

A: B:

Fillinthetabletotheright

9.Aballisthrownhorizontallyataspeedof14meterspersecond(A)fromthetopofacliff.Iftheballhitstheground4.0seconds(B)later,approximatelyhowhighisthecliff?

Whatisthequestionaskingfor?

Whatarethehiddenorunstatedvariables?

A: B:

Fillinthetabletotheright

HorizontallyLaunchedProjectilePracticeWhathappensinthexdimensionstaysinthexdimension

Whathappensintheydimensionstaysintheydimension

Whatdoesthismean?Usethetableattheright.

Aprojectileislaunchedhorizontallyat20m/s.Foursecondslaterithitstheground.

Whatistherangeoftheprojectile(dxordy)?

WhichvishouldIusetogettherange?Whicha?

Solvefortherange.

Whatistheinitialheightoftheprojectile(dxordy)?

WhichvishouldIusetogettherange?Whicha?

Solvefortheheight.

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10.Acannonballlauncheshorizontallyoffatallcliffat40m/s.Anotherballisdropped.Whichonewillhitthegroundfirst?Why?

After4seconds,whatistherangeofthecannonball?

Ifatrainwastravelingat40m/s,howfarwouldthattravelin4seconds?Howdoesthiscomparetothecannonball?

11.TheEnolaGayistravelinghorizontallyat75m/satanaltitudeof9470m,whenitdropsthebomb.

Whatistheinitialhorizontalandverticalvelocityofthebomb?

Createamotion/dotdiagramalongthetopfortheplane.

Createamotiondiagramforthebombdroppedunderneathit.

Whatdoesthismeanfortheplaneandthebomb?Whereistheplanewhenthebombhitstheground?

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12.Aplaneisflyinghorizontallyatanaltitudeof1200mataspeedof150m/s.Itdropsapackagetolandonanisland.Howfarawayfromtheislandshouldtheplanebewhenitreleasesthepackage?(Hint:Createatable.Youmayneedtofindsomethingincommonbetweenxandy)

13.Threecannonsfirethreedifferentcannonballshorizontallyoffthetopofthesame30metertallcliffdifferentvelocitiesasshowninthetablebelow.

CannonBall Velocity(m/s)

A 40m/s

B 70m/s

C 90m/s

a)Whichcannonballhitsthegroundfirst?Howdoyouknow?

b)WhatisthehorizontalvelocityofCannonBallAafter2seconds?

c)WhatisthehorizontalcomponentofCannonBallBsvelocitywhenithitsthe ground?

d)HowlongdoesittakeforCannonBallCtohittheground?

e)WhatisthehorizontalrangeofCannonBallC?

14.Aplaneisflyinghorizontallyat120m/swhenitreleasesapackage.Thepackagecrashlandsonanisland12.7secondslater.

a)Whatisthehorizontalcomponentofthepackagesvelocity

theinstantithitstheground?

b)Whatistheverticalcomponentofvtheinstantithitstheground?

c)Whatistheresultantvelocitytheinstantithitstheground?

VectorComponents

Intohowmanycomponentscanavectorbesplit?

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15.Asoccerballiskickedat25degreesfromthehorizontalwithaninitialvelocityof25m/s.

a)Whatisthexcomponentoftheballsinitialvelocity?

b)Whatistheycomponentoftheballsinitialvelocity?

16.Alittleboypullsawagonwithaforceof17Natanangleof23degrees.

a)Whatisthehorizontalcomponentoftheboysforce?

b)Whatistheverticalcomponentoftheboysforce?

3.Gravitypullsdownontheboxtotherightwithaforceof100N.

a)Whatisthecomponentoftheforceparalleltotheincline?

b)Whatisthecomponentoftheforceperpendiculartotheincline?

ProjectileMotion2:GroundLaunchedProjectilesGroundlaunchedprojectilesarejustlikehorizontallylaunchedprojectiles,exceptthatvinitialisnotcompletelyhorizontal(viydoesntequalzero).

17.Acannonfiresashotwithaninitialvelocityof80m/satanangle27degreesabovethehorizontal

a)Whatisthehorizontalcomponentoftheinitialvelocity?(makeasketch)

b)Whatistheverticalcomponentoftheinitialvelocity?

c)Atthepeakofthetrajectory,whatisthehorizontalcomponentofthevelocity?

d)Atthepeakofthetrajectory,whatistheverticalcomponentofthevelocity?

e)Howmuchtimedoesittaketheprojectiletoreachthepeak?

(Makeatable.Includevf)

18.Abaseballishitwithaninitialvelocityof35meterspersecondatanangleof18abovehorizontal.

a)Calculatetheverticalcomponentoftheballsinitialvelocity

b)Howmuchtimewillittakethebaseballtoreachthetopofitsflight?

c)Howmuchtotaltimewillthebaseballspendintheair?

19.Aplacekickerstrikesafootballwithahorizontalvelocityof22meterspersecondandverticalvelocityof10meterspersecond.Theballreachesitsmaximumheightwithin1.02seconds.

a)Whatisthetotaltimethattheballwillspendintheair?

b)Calculatethehorizontaldistancethatthefootballwilltravelduringitsflight.

20.Aballisthrownwithaninitialvelocityof15meterspersecondatanangleof20abovethehorizontal.

a)Determinetheverticalcomponentoftheballsinitialvelocity.

b)Determinetheballstotaltimeofflight.

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GroundLaunchedProjectilePracticeForanyprojectilemotion,weknowthat:

21.Asoccerballiskickedwithaninitialvelocityof20m/satanangleof30degrees

a)Whatisthehorizontalcomponentoftheinitialvelocity?

b)Whatistheverticalcomponentoftheinitialvelocity?

Acceleration

HorizontalVelocity

VerticalVelocity

c)Whatisthehorizontalcomponentofvelocityatthepeak?

d)Whatistheverticalcomponentofvelocityatthepeak?

e)Whatisthehorizontalcomponentofvelocityattheend?

f)Whatistheverticalcomponentofvelocityattheend?

g)Howmuchtimedoesittaketheballtoreachthepeak?

h)Howmuchtotaltimedoestheballspendintheair?

i)Whatisthemaximumheighttheballreaches?

j)Whatisthetotalrangeoftheball?

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Whydowesplitintoxandycomponents?Aprojectileislaunchedat39.2m/satanangleof30degreesfromhorizontal

22.Abaseballishitwithaninitialvelocityof35meterspersecondatanangleof18abovehorizontal.

a.Sketchthebaseballstrajectory.Indicatethepointatwhichtheballsverticalvelocityis0.

b.Calculatetheverticalcomponentoftheballsinitialvelocity.

c.Calculatethetimethatitwilltakefortheballtoreachthetopofitsflight.Explainhowthisamountoftimeisrelatedtothetotalamountoftimethattheballwillremainintheair.

d.Calculatethemaximumheightthattheballwillreach.

23.Aplacekickerstrikesafootballwithahorizontalvelocityof22meterspersecondandverticalvelocityof10meterspersecond.Theballreachesitsmaximumheightwithin1.02seconds.

a.Whatisthetotaltimethattheballwillspendintheair?

b.Calculatethehorizontaldistancethatthefootballwilltravelduringitsflight.

24.Aballfliesthroughaparabolicpathandpassesthroughpoin