Imagine a ball dropped from a height of 15 feet. Each time it strikes the ground, it bounces 0.6 times as high as the previous bounce. Find the total distance the ball will travel if it is allowed to bounce indefinitely.
A) 9 feet
B) 0.4 feet
C) 60 feet
D) 15 feet

Question

Quizplus · Accepted Answer

Each time the ball bounces, it travels two times the height of the previous bounce (once up, and once down). Therefore, the total distance the ball will travel is equal to:
15 + 2(0.6)(15) + 2(0.6)^2(15) + 2(0.6)^3(15) + ... 
= 15 + 18 + 12.96 + 9.3654 + ...
This is an infinite geometric series with first term (a) = 15 and common ratio (r) = 0.6.
The sum of an infinite geometric series is given by: 
S = a/(1 - r)
= 15/(1 - 0.6)
= 60
Therefore, the total distance the ball will travel is 60 feet.

Imagine a Ball Dropped from a Height of 15 Feet