Need help finding the total distance traveled?

Question

A ball drops from a height of 21 feet. Each time it hits the ground, it bounces up 25 percents of the height it fall. Assume it goes on forever, find the total distance it travels.

Answer 1

If the ball never stops bouncing, it never stops traveling.  Therefore, there is no total distance traveled. It isn't covering much distance but it is still bouncing. You answered your own question.

Answer 2

Whatever Max says - he always votes for himself twice anyway

Answer 3

Infinite , because each bounce it will loose 1/4 height ,gradually it  stand to be zero , but shall never be zero.

Answer 4

well this is an infinite (it has infinitely many terms) geometric (all the terms are related by a constant multiple or ratio) series, and the formula for the sum of an infinite series is

s=a/(1-r) if -1<r<1

r is the common ratio (in this case 1/4 since it bounces up 25% of its height each time)

a is the starting value, in this case 21 feet

s=21/(1-1/4)

s=21/(3/4)

s=21*(4/3)

s=7*4

s=28 feet