1. A rubber ball is dropped from a height of 2.0m. After each bounce it returns

Question

1. A rubber ball is dropped from a height of 2.0m. After each bounce it returns to a height of 2/3 its starting height.
(i) Determine the height the ball returns to after its third bounce.
(ii) What is the ball’s velocity just before it bounces the second time?
(iii) From what height would the ball need to be dropped in order to have a speed of 30 m/s just before its first bounce?

Im stuck on what to do. I got number 1 already with a height of 0.593m. I believe that to be the answer to the first question. Could you help with the rest and if possible check to see if i got the first part correct?

Thank you

Explanation / Answer

First we find the coefficient of restitution, e = h2/h1 = 2/3 = 0.81 (i) the height of ball after 3rd rebound h' = e^2*4/3 = 0.88 m (ii) the speed before 2nd bouncing V = e*2*9.8*1.33 V = 4.14 m/s (iii) the bouncing speed V = e*2*g*h (30/0.88)^2 = 2*9.8*h h = 59.29 m the height would the ball need to be dropped in order to have a speed of 30 m/s just before its first bounce is 59.29 m.

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