(Figure 1) shows a friend standing on the roof of a building that is 51.8 m tall

Question

(Figure 1) shows a friend standing on the roof of a building that is

51.8 m tall. The roof is square and measures 20 m on a side. You want to shoot a paintball so that it lands on the roof and startles your friend, using a gun that shoots paintballs at a muzzle speed of 42 m/s. The only problem is a slim billboard 67.5 m high between you and the roof, 20 m in front of the building. You position yourself in front of the billboard such that when you hold the gun 1.5 m above the ground and fire, the paintball just barely gets over the billboard at the highest point in its trajectory.

Part A

At what angle ? above the horizontal do you need to shoot the ball to clear the billboard?

Express your answer using two significant figures.

Part B

What is your horizontal distance from the billboard?

Express your answer with the appropriate units.

Part C

How long does the paintball take to move from the highest point in its trajectory to the height of the roof?

Express your answer with the appropriate units

Part D

Does the ball strike the roof?

Yes or No, Explain.

Part E

What is the speed of the ball when it strikes?

Express your answer with the appropriate units.

(Figure 1) shows a friend standing on the roof of a building that is 51.8 m tall. The roof is square and measures 20 m on a side. You want to shoot a paintball so that it lands on the roof and startles your friend, using a gun that shoots paintballs at a muzzle speed of 42 m/s. The only problem is a slim billboard 67.5 m high between you and the roof, 20 m in front of the building. You position yourself in front of the billboard such that when you hold the gun 1.5 m above the ground and fire, the paintball just barely gets over the billboard at the highest point in its trajectory. art A At what angle ? above the horizontal do you need to shoot the ball to clear the billboard? Express your answer using two significant figures. Part B What is your horizontal distance from the billboard? Express your answer with the appropriate units. Part C How long does the paintball take to move from the highest point in its trajectory to the height of the roof? Express your answer with the appropriate units Part D Does the ball strike the roof? Yes or No, Explain. Part E What is the speed of the ball when it strikes? Express your answer with the appropriate units.

Explanation / Answer

A> . max. height = 67.5 - 1.5 =66 m

u^2 sin^@ /2g = 66

sin@ = sqrt(2g66) /42 = 0.856

@ = 58.91 m

B. max. height is at half distance of range.

d = R/2 = u^2sin(2@) /2g = 42^2 x sin(2x58.91) / 2g

d = 79.60 m

C> .
in vertical it have to move ( 67.5 - 51.8) = 15.7 m downwards

using h = ut + at^2 /2 in vertical diorection,

- 15.7 = 0 - 9.8t^2 /2

t = 1.79 sec

D>. in this time distancetraveled in horizontal direction

d = 42cos58.91 x 1.79 = 38.82 m which is greater than 20 m

so, YES.

E>. vy = 9.8 x 1.79 =17.54 m/s

vx = 42cos58.91 =21.69 m/s

speed = sqrt(vx^2 + vy^2) =27.89 m/s

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