A tennis ball dropped from a height 30m bounces 40% of the height from which it felt on its bounce. what is the vertical distance it travels before coming to rest.

Answer 1

let us assume that the ball is at rest when it bounces less than 1mm.

Starting at 30,000 mm, we find that on the 12th bounce it has "stopped" bouncing.

So, with r=0.4, and noting that 12 bounces involve a round trip (up and down), we have the sum of a geometric sequence:

30 + 2*30(1-.4^12)/(1-.4) = 130m