Question

A ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.81h feet. Find the total distance traveled by the ball.

Answer 1

The first drop makes the ball travel 16 m.
Then the maximum height decreases to 16 x 0.81
And the distance traveled is twice the distance traveled.
If we make a pattern, this forms a geometric progression in which the common ratio is 0.81 and the first term is 16.
The sum of this series: a / (1 - r)
= 16 ( 1 - 0.81)
= 84 feet
This is the upward height, and the ball returns every time so:
Total distance = 84 x 2
= 168 feet