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Example Problems

4.1 Projectile Motion• Example1:-Whileplayingwithahotwheelcaramonkeygivesthecarabigpushsendingthecarflyingofftheedgeofatablewithahorizontalvelocityof1.2m/s.Ifthecarlands0.51mfromtheedgeofthetable,whatistheheightofthetable?

What are the givens and unknowns? Write your formulas and show your workVertical

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vov =

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• Example2:-Acrazymonkeythrowsyourcarkeysofftheedgeofacliffwithahorizontalvelocityof3.50m/s.Ifthekeyslandsonthegroundahorizontaldistanceof5.40mfromtheedgeofthecliff,whatistheheightofthecliff?

What are the givens and unknowns? Write your formulas and show your workVertical

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g =

€

vov =

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v fv =

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• Example3:-Suppliesaredroppedfromaplaneinordertohelpsomepeoplestrandedonadesertisland.Iftheplaneisflyingataaltitudeof300mwithahorizontalspeedof60.0m/s,howfarbeforethedropzoneshouldthesuppliesbereleased?

What are the givens and unknowns? Write your formulas and show your workVertical

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g =

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vov =

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v fv =

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Δh =

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t =

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vh =

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Δdh =

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Draw a sketch as seen from an observer on the ground

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• Example4:-InthemovieTheGodsMustBeCrazyapilotdropsanemptyCoca-Colabottleofoutofanairplane.Itisrecoveredbyanativebelow,whothinksitisamessagefromthegods.Iftheplanefromwhichthebottlewasdroppedwasflyingatanaltitudeof500m,andthebottlelands400mhorizontallyfromtheinitialdroppingpoint,howfastwastheplaneflyingwhenthebottlewasreleased?

What are the givens and unknowns? Write your formulas and show your workVertical

€

g =

€

vov =

€

v fv =

€

Δh =

€

t =

Horizontal

€

vh =

€

Δdh =

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t =

Draw a sketch as seen from an observer on the ground

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Doc Fizzix ExampleProblems•ProjectileMotion

Chapter 4 Motion in Two Dimensions

• Example5:-DiversinAcapulcodivefromacliffthatis61mhigh.Iftherocksbelowthecliffextendoutwardfor23m,whatistheminimumhorizontalvelocityadivermusthaveinordertocleartherocksbellow?

What are the givens and unknowns? Write the formula and show your workVertical

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g =

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vov =

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• Example6:-Monkeysloveplayingdarts.Amonkeythrowsadarthorizontallywithaspeedof12.4m/s.Thedarthitsthedartboard0.32mbelowtheheightfromwhichitwasthrown.Howfarawayisthemonkeyfromthedartboard?

What are the givens and unknowns? Write the formula and show your workVertical

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g =

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vov =

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v fv =

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Δh =

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t =

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Student Problems

4.1 Projectile MotionYOU MUST SHOW ALL WORK! (Formulas, plug in numbers, answer boxed, units)

1. Amonkey throws Justin Bieber off the balcony of his apartment. If themonkeythrowsthe“TheBiebs”withahorizontalvelocityof1.5m/s,and“TheBiebs”landsonthegroundahorizontaldistanceof8mfromtheedgeofthebalcony.Howlongwasthe“TheBiebs”intheairandwhatistheheightofthebalcony?

Show your work:

What are the givens and unknowns?

Draw a picture showing distance, height, and velocity.

Write the vertical formula

Write the horizontal formulaVertical

€

g =

€

vov =

€

v fv =

€

Δh =

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t =

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€

vh =

€

Δdh =

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t =

a) b)

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2. Abaseballleavesthehandofatopprofessionalpitchertravelingat44.7m/s(100mph).Thedistancefromthepitchersmoundtothehomeplateis18.29-m.Howmuchtimedoesabatterhavetoreacttotheballandhowfarverticallywilltheballhavedroppedonceitcrosseshomeplate?

Show your work:

What are the givens and unknowns?

Draw a picture showing distance, height, and velocity.

Write the vertical formula

Write the horizontal formulaVertical

€

g =

€

vov =

€

v fv =

€

Δh =

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t =

Horizontal

€

vh =

€

Δdh =

€

t =

a) b)

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3. Arockisthrownhorizontallyataspeedof24m/sfromthetopofacliff.Iftherockhitstheground3.5secondslater,howfarfromtheedgeofthecliffdidtherocklandandapproximatelyhowhighisthecliff?

Show your work:

What are the givens and unknowns?

Draw a picture showing distance, height, and velocity.

Write the vertical formula

Write the horizontal formulaVertical

€

g =

€

vov =

€

v fv =

€

Δh =

€

t =

Horizontal

€

vh =

€

Δdh =

€

t =

a) b)

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4. Agorilladesignsafancynerfgunthathasamuzzlevelocityof250m/s.Inanerfgunwarbetweenamonkeyandagorillaadartisfiredhorizontallyfroma2meterheightbythegorillatowardsthemonkeybutmonkeyducksjustintimeandthedartgoesflyingpastthemonkey.Howfarwillthedarttravelbeforestrikingthegroundandhowlongitthedarthavebeenintheair?

Show your work:

What are the givens and unknowns?

Draw a picture showing distance, height, and velocity.

Write the vertical formula

Write the horizontal formulaVertical

€

g =

€

vov =

€

v fv =

€

Δh =

€

t =

Horizontal

€

vh =

€

Δdh =

€

t =

a) b)

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5. DuringworldwarIItheB-17bomber(TheFlyingFortress)wasinstrumentaltothevictoryachievedbythealliedforcesagainstGermany. Ifflyingatatopspeedof128.3m/s(287mph)andatanaltitudeof3,000-m(10,000feet),howlongwouldittakeabombdroppedfromitscargobaytohitthegroundandatwhatdistancebeforeit’sintendedtargetwouldthebomberneedtoreleaseit’sloadinordertohitthetarget?

Show your work:

What are the givens and unknowns?

Draw a picture showing distance, height, and velocity.

Write the vertical formula

Write the horizontal formulaVertical

€

g =

€

vov =

€

v fv =

€

Δh =

€

t =

Horizontal

€

vh =

€

Δdh =

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t =

a) b)

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Chapter 4 Motion in Two Dimensions

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6. Arifleisaimedhorizontallyatatargetlocated30-maway.Thebullethitsthetargetfalling 0.0191-m below the original horizontal aiming point. How longwas thebulletintheairandwhatwastheoriginalmuzzlevelocityofthebullet?

Show your work:

What are the givens and unknowns?

Draw a picture showing distance, height, and velocity.

Write the vertical formula

Write the horizontal formulaVertical

€

g =

€

vov =

€

v fv =

€

Δh =

€

t =

Horizontal

€

vh =

€

Δdh =

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t =

a) b)

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Chapter 4 Motion in Two Dimensions

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7. Apoliceofficerischasingamonkeyacrossarooftop,botharerunningat4.5m/s.Themonkeycomestotheedgeofthebuildingandtheonlychanceforescapeistojumptothenextbuilding.Thenextbuildingis4.8mverticallybellowand6.2mawayhorizontally.Ifthemonkeytriestomakethejump,willhemakeittothenextbuildingorwillhefallshort?(Hint:calculatehowfarhorizontallythemonkeytravelsthencompareyourcalculatesvaluetotheactualdistancebetweenthebuildings.)

Show your work:

What are the givens and unknowns?

Draw a picture showing distance, height, and velocity.

Write the vertical formula

Write the horizontal formulaVertical

€

g =

€

vov =

€

v fv =

€

Δh =

€

t =

Horizontal

€

vh =

€

Δdh =

€

t =

a)

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8. Monkeysloveplayingdarts.Amonkeyclaimsthathecanthrowadartandhita0.05-mdiameterbulls-eyeonadartboardlocated2.0metersaway.Themonkeystartshisthrowbylininguphisdartevenwiththetopedgeofthebulls-eye.Thedartleavesthemonkey’shandtravelinghorizontalwithaspeedof15m/s.Calculatehowfarthedartfallsbellowthetopedgeofthebulls-eye.Doesthedartlandinsideofthebulls-eyeasthemonkeyclaimsorbellowthebulls-eye?

Show your work:

What are the givens and unknowns?

Draw a picture showing distance, height, and velocity.

Write the vertical formula

Write the horizontal formulaVertical

€

g =

€

vov =

€

v fv =

€

Δh =

€

t =

Horizontal

€

vh =

€

Δdh =

€

t =

a) b)

Doc Fizzix StudentProblems•ProjectileMotion

Chapter 4 Motion in Two Dimensions