Question

A ball is dropped from a height of 6 feet and begins bouncing. The height of each bounce is three-fourths the height of the previous bounce. Find the total vertical distance the ball travels before coming to rest?

Answer 1

theoretically, the answer is infinity. however, in a non perfect universe such as our own, practically the answer would be around 17ft.

Answer 2

The sum to infinity of a geometric sequence where the first term is a and the common ratio r is less than 1 is:
$S_{\infty} =\frac{a}{1-r}$
Using this formula, the total vertical distance the ball travels before coming to rest is given by:
$S_{\infty}=\frac{6}{1-\frac{3}{4}}=24\ feet$