A ball kicked upward reaches a height of 10 feet. Each time it hits the ground, it bounces to two-thirds of its previous height.

Question

What is the distance the ball has travelled when it strikes the ground for the fourth time? What is the total distance travelled by the ball before coming down?

Answer 1

First, let us assume that the ball is bouncing vertically!

The maximum height at each bounce forms a geometric series with first term=10 and ratio=2/3.

The distance traveled at each bound is 2 times maximum height.

Use the sum of a geometric series for 4 terms to get the travel in 4 bounces and the sum of the infinite series to get the travel until the ball stops bouncing.

The sums you need are

4th term : (ar⁵-a)/(1-r) and infinite sum: a/(1-r)