A ball returns to 50% of its preceding height on each bounce. If the ball is tossed to the height of 5m, what is the total distance the ball travels before coming to rest?

Answer 1

It is geometric series:

C (R)^N, N=0,1,2,3,.... infinity

which has sum C/(1-r)

C=5, r=1/2

f(n) = 5 * (1/2)^n, n=0,1,2,3,....infinity

The sum is 5/ (1 - 1/2) = 5/(1/2) = 5/1 *2/1 =10