Assume UP is POSITIVE in this problem. A 62.4-g basketball rolls down a roof and

Question

Assume UP is POSITIVE in this problem. A 62.4-g basketball rolls down a roof and falls to the ground 21.71 m below. The roof is angled at 8 degrees below horizontal and the ball reaches a speed of 5.8 m/s just as it leaves the edge of the roof. What is the initial x and y-velocity of the ball as it begins its flight? horizontally; vertically What is the final y-velocity of the ball, the instant before it hits the ground? How long was the ball in the air? How far from the building did the ball land?

Explanation / Answer

a.

initial vertial velocity, U y= - u sin 8 = - 5.8* sin 8 = - 0.807 m/s (ans)

Initial Horizontal velocity, Ux= u cos 8= 5.743 m/s (ans)

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b.

Using second equation of motion

h= Uy*t+0.5*9.8* t^2

21.71= 0.807* t + 4.9 t^2

Solving for t

t= 2.02 second

Final velocity in y direction before hitting the ground,

Vy= -(Uy+gt)

= -(0.807+ 9.8* 2.02)

= - 20.603 m/s (ans)

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c.time of flight, t= 2.02 seconds (ans)

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d. Horizontal distance from building

R= Ux*t= 5.743* 2.02

R= 11.6 m

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Comment in case any doubt..goodluck

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