Problem A ball of mass m = 8 kg is dropped from rest at a height h = 13.1 m abov

Question

Problem A ball of mass m = 8 kg is dropped from rest at a height h = 13.1 m above the ground. Ignore air resistance.

A. Determine the speed of the ball when it is at a height y = 2.9 m above the ground.

B. Determine the speed of the ball at y = 2.9 m if it is given an initial downward speed vi = 3.6 m/s at the initial altitude h.

(a) If the ball is being released with a downward speed 4.9 m/s initially, what will be its final speed when it hits the table 0.8 m below the release point?

(b) If the ball is being thrown upwards instead with the same speed 4.9 m/s, what is the final speed when it hits the table?

Explanation / Answer

speed of a falling object v = sqrt(2gh)

the ball falls from 13.1 m to 2.9 m

h = 13.1 -2.9 = 10.2 m

v = sqrt(2*9.8*10.2) = 14.14 m/s

B) if the ball has an intial vel u then final velocity

vf2 = vi2 +2gh

        = 3.62 + 2*9.8*10.2 = 212.88

final velocity vf (y=2.9m)   = 14.59 m/s

a) initial vel   vi = 4.9 m/s

height fallen h = 0.8 m

vf2 = 4.92 + 2*9.8 *0.8

vf = 6.3 m/s

(a) if the ball is thrown upward with a vel of 4.9 m/s , it will reach a maximum height till it vertical vel -0 and then falls down from that height, as the enrgy is conserved, it will regain the original velocity when it is its original point and move downward with 4.9 m.s

the final vel. is same as the case of (a)

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