MasteringPhysics - Assignment 5 - Motion in 2-D
MasteringPhysics - Assignment 5 - Motion in 2-D
MasteringPhysics - Assignment 5 - Motion in 2-D
AdvicefortheQuarterback
Aquarterbackissetuptothrowthefootballtoareceiverwhoisrunningwithaconstantvelocityv r directlyawayfromthe
quarterbackandisnowadistanceDawayfromthequarterback.Thequarterbackfiguresthattheballmustbethrownatan
angletothehorizontalandheestimatesthatthereceivermustcatchtheballatimeintervaltc afteritisthrowntoavoidhaving
oppositionplayerspreventthereceiverfrommakingthecatch.Inthefollowingyoumayassumethattheballisthrownand
caughtatthesameheightabovethelevelplayingfield.Assumethattheycoordinateoftheballattheinstantitisthrownor
caughtisy = 0andthatthehorizontalpositionofthequarterbackisx = 0.
Usegforthemagnitudeoftheaccelerationduetogravity,andusethe
picturedinertialcoordinatesystemwhensolvingtheproblem.
PartA
Findv 0y ,theverticalcomponentofthevelocityoftheballwhenthequarterbackreleasesit.
Hint1.Equationofmotioninydirection
Whatistheexpressionfory(t),theheightoftheballasafunctionoftime?
Answerintermsoft,g,andv 0y .
ANSWER:
1 2
y(t) = v0y t gt
2
Hint2.Heightatwhichtheballiscaught,y(tc )
Rememberthataftertimetc theballwascaughtatthesameheightasithadbeenreleased.Thatis,y(tc ) = y0 = 0
ANSWER:
v 0y = 0.5gt c
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10/4/2017 MasteringPhysics: Assignment 2: Motion in 2-D
Correct
PartB
Findv 0x ,theinitialhorizontalcomponentofvelocityoftheball.
Hint1.Receiver'sposition
Findxr ,thereceiver'spositionbeforehecatchestheball.
AnswerintermsofD,v r ,andtc .
ANSWER:
xr = D + vr tc
Hint2.Football'sposition
Findxc ,thehorizontaldistancethattheballtravelsbeforereachingthereceiver.
Answerintermsofv 0x andtc .
ANSWER:
xc = v 0x t c
ANSWER:
D+vr t c
v 0x =
tc
Correct
PartC
Findthespeedv 0 withwhichthequarterbackmustthrowtheball.
AnswerintermsofD,tc ,v r ,andg.
Hint1.Howtoapproachtheproblem
RememberthatvelocityisavectorfromsolvingPartsAandByouhavethetwocomponents,fromwhichyoucan
findthemagnitudeofthisvector.
ANSWER:
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10/4/2017 MasteringPhysics: Assignment 2: Motion in 2-D
2
2
D
v0 = sqrt{(.5gtc ) +(
tc
+ vr ) }
Correct
PartD
Assumingthatthequarterbackthrowstheballwithspeedv 0 ,findtheangleabovethehorizontalatwhichheshouldthrow
it.
Yoursolutionshouldcontainaninversetrigfunction(enteredasasin,acos,oratan).Giveyouranswerinterms
ofalreadyknownquantities,v 0x ,v 0y ,andv 0 .
Hint1.Findanglefromv0x andv0y
ThinkofvelocityasavectorwithCartesiancoordinatesv 0x x
^andv 0y y
^.Findtheanglethatthisvectorwouldmake
withthexaxisusingtheresultsofPartsAandB.
ANSWER:
v0y
= atan{
v
}
0x
Correct
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