PHY111–Chapter3–Problems–Vectors&2-DimensionalMotion
1.VectorAhasamagnitudeof29unitsandpointsinthepositivey-direction.WhenvectorBisaddedtovectorA,
theresultantvector,A+B,pointsinthenegativey-directionwithamagnitudeof14units.Findthemagnitudeand
directionofvectorB.
3.VectorAis3.00unitsinlengthandpointsalongthepositivex-axis.VectorBis4.00unitsinlengthandpoints
alongthenegativey-axis.Usegraphicalmethodstofindthemagnitudeanddirectionofthevectors(a)A+B,and
(b)A–B.
5.Arollercoastermoves200fthorizontallyandthenrises135ftatanangleof30.00abovethehorizontal.Next,it
travels 135 ft at an angle of 40.00 below the horizontal. Use graphical techniques to find the roller coaster’s
displacementfromitsstartingpointtotheendofthismovement.
7.AplanefliesfrombasecamptolakeA,adistanceof280kmatadirectionof20.00northofeast.Afterdropping
offsupplies,theplanefliestolakeB,whichis190kmand30.00westofnorthfromlakeA.Graphicallydetermine
thedistanceanddirectionfromlakeBtothebasecamp.
9. A man in a maze makes three consecutive displacements. His first displacement is 8.00 m westward, and the
secondis13.0mnorthward.Attheendofhisthirddisplacementheisbacktowherehestarted.Usethegraphical
methodtofindthemagnitudeanddirectionofhisthirddisplacement.
11.ThemagnitudeofvectorAis35.0unitsandpointsinthedirection3250counterclockwisefromthepositivexaxis.Calculatethex-andy-componentsofthisvector.
13.Agirldeliveringnewspaperscoversherroutebytraveling3.00blockswest,4.00blocksnorth,andthen6.00
blockseast.(a)Whatisherresultantdisplacement?(b)Whatisthetotaldistanceshetravels?
16. A quarterback takes the ball from the line of scrimmage, runs backwards for 10.0 yards, then runs sideways
parallel to the line of scrimmage for 15.0 yards. At this point, he throws a 50.0-yard forward pass straight
downfield,perpendiculartothelineofscrimmage.Whatisthemagnitudeofthefootball’sresultantdisplacement?
18.AmapsuggeststhatAtlantais730milesinadirection5.000northofeastfromDallas.Thesamemapshowsthat
Chicagois560milesinadirection21.00westofnorthfromAtlanta.Thefigureshowsthelocationofthesethree
cities.ModelingtheEarthasflat,usethisinformationtofindthedisplacementfromDallastoChicago.
19.Acommuterairplanestartsfromanairportandtakestherouteshowninthefigurebelow.Theplanefliesto
cityA,located175kmawayinadirection30.00northofeast.Next,itfliesfor150km20.00westofnorth,tocityB.
Finally,theplaneflies190kmduewest,tocityC.FindthelocationofcityCrelativetothelocationofthestarting
point.
20.Thehelicopterviewinthefigurebelowshowstwopeoplepullingonastubbornmule.Find(a)thesingleforce
thatisequivalenttothetwoforcesshownandb)theforceathirdpersonwouldhavetoexertonthemuletomake
thenetforceequaltozero.TheforcesaremeasuredinunitsofNewtons(N).
22.Oneofthefastestrecordedpitchesinmajor-leaguebaseball,thrownbyTimLincecumin2009,wasclockedat
101.0mi/hr.Ifapitchwerethrownhorizontallywiththisvelocity,howfarwouldtheballfallverticallybythetime
itreachedhomeplate,60.5ftaway?
23.Astudentstandsattheedgeofacliffandthrowsastonehorizontallyovertheedgewithaspeedof18.0m/s.
Thecliffis50.0maboveaflat,horizontalbeachasshowninthefigurebelow.(a)Whatarethecoordinatesofthe
initialpositionofthestone?(b)Whatarethecomponentsoftheinitialvelocity?(c)Writetheequationsforthex-
andy-componentsofthevelocityofthestonewithtime.(d)Writetheequationsforthepositionofthestonewith
time,usingthecoordinatesshowninthefigurebelow.(e)Howlongafterbeingreleaseddoesthestonestrikethe
beachbelowthecliff?(f)Withwhatspeedandangleofimpactdoesthestoneland?
24.Arockisthrownupwardfromthelevelgroundinsuchawaythatthemaximumheightofitsflightisequaltoits
horizontalrangeR.(a)Atwhatangleθistherockthrown?(b)IntermsoftheoriginalrangeR,whatistherange
Rmaxtherockcanattainifitislaunchedatthesamespeedbutattheoptimalangleformaximumrange?(c)Would
youranswertopart(a)bedifferentiftherockisthrownwiththesamespeedonadifferentplanet?Explain.
25. The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 m when leaving the
groundatanangleof450.Withwhatspeedmusttheanimalleavethegroundtoreachthatheight?
27.Aplace-kickermustkickafootballfromapoint36.0m(about40yards)fromthegoal.Halfthecrowdhopes
theballwillclearthecrossbar,whichis3.05mhigh.Whenkicked,theballleavesthegroundwithaspeedof20.0
m/satanangleof53.00tothehorizontal.(a)Byhowmuchdoestheballclearorfallshortofclearingthecrossbar?
(b)Doestheballapproachthecrossbarwhilestillrisingorwhenfalling?
29.Abrickisthrownupwardfromthetopofabuildingatanangleof250tothehorizontalandwithaninitialspeed
of15m/s.Ifthebrickisinflightfor3.0s,howtallisthebuilding?
30.Anartilleryshellisfiredwithaninitialvelocityof300m/sat55.00abovethehorizontal.Toclearanavalanche,
itexplodesonamountainside42.0safterfiring.Whatarethex-andy-coordinatesoftheshellwhereitexplodes,
relativetoitsfiringpoint?
31.Acarisparkedonacliffoverlookingtheoceanonaninclinethatmakesanangleof24.00belowthehorizontal.
Thenegligentdriverleavesthecarinneutral,andtheemergencybrakesaredefective.Thecarrollsfromrestdown
theinclinewithaconstantaccelerationof4.00m/s2foradistanceof50.0mtotheedgeofthecliff,whichis30.0m
abovetheocean.Find(a)thecar’spositionrelativetothebaseofthecliffwhenthecarlandsintheoceanand(b)
thelengthoftimethecarisintheair.
32.Afiremand=50.0mawayfromaburningbuildingdirectsastreamofwaterfromaground-levelfirehoseatan
angleofθi=30.00abovethehorizontal,asshowninthefigurebelow.Ifthespeedofthestreamasitleavesthehose
isvi=40.0m/s,atwhatheightwillthestreamofwaterstrikethebuilding?
33. A projectile is launched with an initial speed of 60.0 m/s at an angle of 30.00 above the horizontal. The
projectilelandsonahillside4.00slater.Neglectairfriction.(a)Whatistheprojectile’svelocityatthehighestpoint
ofitstrajectory?(b)Whatisthestraight-linedistancefromwheretheprojectilewaslaunchedtowhereithitsits
target?
34. A playground is on the flat roof of a city school, 6.0 m above the street, as shown in the figure below. The
verticalwallofthebuildingish=7.00mhigh,toforma1-mhighrailingaroundtheplayground.Aballhasfallento
thestreetbelow,andapasserbyreturnsitbylaunchingitatanangleofθ=53.00abovethehorizontalatapointd=
24.0mfromthebaseofthebuildingwall.Theballtakes2.20storeachapointverticallyabovethewall.(a)Find
thespeedatwhichtheballwaslaunched.(b)Findtheverticaldistancebywhichtheballclearsthewall.(c)Find
thehorizontaldistancefromthewalltothepointontheroofwheretheballlands.
45.Howlongdoesittakeanautomobiletravelingintheleftlaneofahighwayat60.0km/hrtoovertake(become
evenwith)anothercarthatistravelingintherightlaneat40.0km/hrwhenthecars’frontbumpersareinitially
100mapart?
47.ANordicjumpergoesoffaskijumpatanangleof10.00belowthehorizontal,traveling108mhorizontallyand
dropping55mverticallybeforelanding.(a)Ignoringfrictionandaerodynamiceffects,calculatethespeedneeded
bytheskieronleavingtheramp.(b)OlympicNordicjumperscanmakesuchjumpswithajumpspeedof23.0m/s,
whichisconsiderablylessthantheanswerfoundinpart(a).Explainhowthisispossible.
48. In a local diner, a customer slides an empty coffee cup down the counter for a refill. The cup slides off the
counterandstrikestheflooratadistancedfromthebaseofthecounter.Iftheheightofthecounterish,(a)findan
expressionforthetimetittakesthecuptofalltothefloorintermsofthevariableshandg.(b)Withwhatspeed
does the cup leave the counter? Answer in terms of the variables d, g, and h. (c) In the same terms, what is the
speed of the cup immediately before it hits the floor? (d) In terms of h and d, what is the direction of the cup’s
velocityimmediatelybeforeithitsthefloor?
51. A rocket is launched at an angle of 53.00above the horizontal with an initial speed of 100 m/s. The rocket
movesfor3.00salongitsinitiallineofmotionwithanaccelerationof30.0m/s2.Atthistime,itsenginesfailand
therocketproceedstomoveasaprojectile.Find(a)themaximumaltitudereachedbytherocket,(b)itstotaltime
offlight,and(c)itshorizontalrange.
55.Ahomerunishitinsuchawaythatthebaseballjustclearsawall21mhigh,located130mfromhomeplate.
Theballishitatanangleof350tothehorizontal,andairresistanceisnegligible.Find(a)theinitialspeedofthe
ball,(b)thetimeittakestheballtoreachthewall,and(c)thevelocitycomponentsandthespeedoftheballwhenit
reachesthewall.(Assumetheballishitataheightof1.0mabovetheground.)
57.Aquarterbackthrowsafootballtowardareceiverwithaninitialspeedof20m/satanangleof300abovethe
horizontal. At that instant the receiver is 20 m from the quarterback. In (a) what direction and (b) with what
constantspeedshouldthereceiverruninordertocatchthefootballatthelevelatwhichitwasthrown?
58.A2.00-mtallbasketballplayerisstandingonthefloor10.0mfromthebasket,asshowninthefigurebelow.If
heshootstheballata40.00anglewiththehorizontal,atwhatinitialspeedmusthethrowthebasketballsothatit
goesthroughthehoopwithoutstrikingthebackboard?Theheightofthebasketis3.05m.
65. A daredevil is shot out of a cannon at 45.00 to the horizontal with an initial speed of 25.0 m/s. A net is
positioned a horizontal distance of 50.0 m from the cannon. At what height above the cannon should the net be
placedinordertocatchthedaredevil?
69.Agolfballwithaninitialspeedof50.0m/slandsexactly240mdownrangeonalevelcourse.(a)Neglectingair
friction,whattwoprojectionangleswouldachievethisresult?(b)Whatisthemaximumheightreachedbytheball,
usingthetwoanglesdeterminedinpart(a)?
73.ThedeterminedWileE.Coyoteisoutoncemoretotrytocapturetheelusiveroadrunner.Thecoyotewearsa
newpairofpowerrollerskates,whichprovideaconstanthorizontalaccelerationof15m/s2,asshowninthefigure
below. The coyote starts off at rest 70 m from the edge of a cliff at the instant the roadrunner zips by in the
direction of the cliff. (a) If the roadrunner moves with constant speed, find the minimum speed the roadrunner
musthavetoreachthecliffbeforethecoyote.(b)Ifthecliffis100mabovethebaseofacanyon,findwherethe
coyotelandsinthecanyon.(Assumehisskatesarestillinoperationwhenheisin“flight”andthathishorizontal
componentofaccelerationremainsconstantat15m/s2.)