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PROJECTILEMOTIONPROBLEMSProblemsdocument
BriefanswerstotheseproblemsareavailableintheAnswersdocument.FullsolutionstotheproblemsareavailableintheSolutionsdocument,andin
theYouTubevideos.Youcanfindlinkstotheseresourcesatmywebsite:
http://www.freelance-teacher.com/videos.htmlLinkstothedocumentsarealsointhevideodescriptionboxesforthe
YouTubevideos.You can support these resources with a monthly pledge of $1 (or more) at my
Patreon page: http://www.patreon.com/freelanceteacher Thisvideoseriesisintendedforstudentswhofindthismaterialtobe
difficult,sointhevideosIproceedslowlyandrepeatmyselfalot.Ifyoufindthevideostomovetooslowly,youcansimplytrytheproblemsinthisProblemsdocument,studythesolutionsintheSolutionsdocument,andskiptoanyparticularpartsofthevideosthatcoveraspectsofthesolutionsthatyoufindconfusing.
Adviceforthosewhofindthismaterialtobedifficult:Youshouldcompletetheproblemsinorder.Takeyourtime.Asabeginner,yourgoalistolearnhowtogettheproblems
right—not,forthetimebeing,howtogettheproblemsrightfast.Don’t“wingit”.Trytousethesamesystematicprocessandnotationinyour
solutionsasIuseinthisSolutionsdocumentandinthevideosolutions.ModelyourscratchworkonthescratchworkillustratedintheseSolutionsandinthevideos.Makeyourscratchworkasneatandcleanaspossible.
Don’tworkinpen.Useapencilwithagooderaser.Alwaysincludeasketchinyoursolution.Makeyoursketchasneatas
possible,andasbigasspacewillallow.Whenpossible,buildthequestionandgivensintoyoursketch.Whenpossible,keepupdatingthesketchthroughoutyoursolutionwithnewinformationthatyoufigureoutinthecourseofyoursolution.
Ifyoudon’tknowhowtosolveaproblemorgetaproblemwrong,then,afterreviewingthesolution,youshouldretrytheproblem,beforemovingontothenextproblemintheseries. Keepredoingeachproblemuntilyoucangetitright. Trytoavoidcarelessmistakes.Doublecheckeachlineyouwritedowninyoursolutionbeforeyouwritedownthenextlineofyoursolution.Yourgoalistolearnhowgetfullcreditoneachproblem.Don’tsettleforpartialcredit—avoidcarelessmistakes! PrintouttheProblemsdocument.Readtheproblemcarefullyatleasttwicebeforebeginningtoworkontheproblem.Rereadtheproblemperiodicallywhileyouaresolvingtheproblemtocheckfordetailsyoumayhavemissedorforgotten.Checktheproblemonemoretimewhenwritingyourfinalanswertobesureyouansweredtherightquestionandansweredallpartsofthequestion.
PROJECTILEMOTIONPROBLEMS Problemsdocument
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Video(1)
Acannonshootsaballwithinitialvelocity20.0m/satanangleof35.0°upwardfromthehorizontal.Theballlandsatahorizontaldistanceof41.0mfromthecannon.WhatistheheightHofthetopofthecannonbarrelabovetheground?
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Video(2)
Avolleyballplayerhitsaballfromoverheadandtowardthefloor.Theballishitwithaninitialspeedofv0=17.0ms-1atadownwardangleofθ=15.0°belowthehorizontal.TheballstrikesthegroundatahorizontaldistanceofR=5.80mfromtheplayer.
(a) WhatwasH,theheightfromwhichtheballwasstruck?(b) Whatisv,thevectorvelocityoftheballwhenithitstheground?Usetheunit
vectorsiandjtoexpressyouranswer.
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Video(3)
Anairplanereleasesapackagewhiledivingatadownwardangleof35.0°belowthehorizontal.Theplaneistravellingataheightof150m,withspeed90.0m/s,whenwhenthepackageisreleased.Howfarawayhorizontallyfromthereleasepointwillthepackagelandontheground?
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Video(4)
Astuntmotorcyclistleavesatakeofframpataspeedof21.0m/s.Therampisinclinedat54.0°tothehorizontal.Thetopoftherampis14.0mhigherthantheground.
(a) Afterjumpingfromtheramp,whathorizontaldistancedoesthemotorcyclisttravelbeforehittingtheground?
(b) Whatisthesmallestvalueofthemotorcyclist’sspeedashefliesthroughtheair?
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Video(5)Afootballiskickedfromgroundlevelata20°anglefromthehorizontal,withinitialspeed25m/s.
(a) Howlongdoesittaketheballtoreachitshighestpoint?(b) Howfarhorizontallydoestheballtravelbeforeithitstheground?(c) Whatisthespeedoftheballrightbeforeithitstheground?(d) Whatisthesmallestvalueoftheball’sspeedoveritsentiretrajectory?
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Video(6)
Agolfballishitfromthegroundintotheair.Theballreachesamaximumheightof25m,andtravelsahorizontaldistanceof215mbeforeithitstheground.
(a) Calculatetheinitialspeedanddirectionwithwhichtheballwashit.(b) Howlongwastheballintheair?(c) Whatisthemagnitudeanddirectionoftheball’saccelerationattheinstant
thatitreachesitsmaximumheight?
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Video(7)
Astuntmotorcyclistleavesahorizontalrampatspeedv0.Therampisataheightofhabovetheground.
(a) WhathorizontaldistanceDfromtherampdoesthemotorcycletravelbeforeithitstheground?
(b) Whatisthespeedvfofthemotorcyclewhenithitstheground?
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Video(8)Aplaneflieshorizontallywithconstantspeedv.TheplanereleasesapackagewhichcoversahorizontaldistanceofDbeforehittingtheground.Whatistheheighthabovethegroundatwhichtheplanewasflyingwhenthepackagewasreleased?
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Video(9)Agolfballishitintotheair.Whenitreachesaheightof34.0mabovetheground,theballismovingataspeedof23m/satanangleof17°abovethehorizontal.
(a) Howfastwastheballinitiallyhit,andatwhatangleabovethehorizontal?(b) Afterbeinghit,howmuchtimedoesittaketheballtoreachaheightof
34.0mabovetheground?(c) Atthatpoint,whatisthehorizontaldistanceoftheballfromthepointat
whichitwashit?
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Video(10)Anairplaneisdivingataconstantspeedatanangleof32°belowthehorizontalwhenitreleasesapackage.Theheightoftheplaneabovethegroundwhenitreleasesthepackageis670m.Thepackageisintheairfor4.5sbeforeithitstheground.
(a) Determinethespeedoftheplane.(b) Whathorizontaldistancedoesthepackagetravelwhileitisfalling?(c) Determinethehorizontalandverticalcomponentsofthepackage’svelocity
justbeforeithitstheground.
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Video(11)Arockisthrown,withinitialspeedv0andangleα,upontoahorizontal,ice-covered,frictionlessroofofwidthD,sothatitjustreachestothetopoftheroof.Itthenslidesacrosstheroofwithconstantspeed,andfallsoffontheotherside.Howmuchtimepassesbetweenthemomentwhentherockisthrown,andthemomentwhenitlandsontheoppositeside?
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Video(12)Arockisthrown,atanangleθ,upontoahorizontal,ice-covered,frictionlessroofofwidth10mandheight4m,sothatthattherocklandsontheroofatthehighestpointofitstrajectory.Therocktakes2.0stoslideacrosstheroofwithconstantspeed,andthenfallsoffontheotherside.
(a) Findtheinitialspeedanddirectionwithwhichtherockwasthrown.(b) FindD,thetotalhorizontaldistancetraveledbytherock.