A certain ball bounces to 2/3 of the height it fell from. If this ball is initially dropped from 27 feet, approximate the total distance the ball travels.

Question

i dunno how to answer that

Answer 1

In this problem, it must be how far the ball travels to get to "rest" which is close to a geometric series:

27 + 2(27)(2/3) + 2(27)(2/3)² + .... = (54 + 54(2/3) + 54(2/3)² + ....) - 27

Now evaluate the infinite sum = a/(1-r) with r = 2/3 and a = 54