A tennis ball is dropped from a height of 15 ft. If the ball rebounds of its height on each bounce, how far will the ball travel before coming to rest?
A) 60 ft
B) 75 ft
C) 30 ft
D) 15 ft
E) 45 ft

Question

A tennis ball is dropped from a height of 15 ft. If the ball rebounds  of its height on each bounce, how far will the ball travel before coming to rest? ​​
A) 60 ft 
B) 75 ft 
C) 30 ft 
D) 15 ft 
E) 45 ft

Quizplus · Accepted Answer

The total distance the ball travels is calculated by adding up the distance it travels during each bounce. The ball rebounds 11/15 of its height, so after the first bounce, it reaches a height of 11/15*15 = 11 ft. It then falls from 11 ft to the ground, for a total distance of 11 ft + 15 ft = 26 ft traveled on the first bounce. On the second bounce, the ball rebounds 11/15*11 = 8.14 ft, and falls from 8.14 ft to the ground, for a total distance of 8.14 ft + 11 ft = 19.14 ft traveled on the second bounce. On the third bounce, the ball rebounds 11/15*8.14 = 5.89 ft, and falls from 5.89 ft to the ground, for a total distance of 5.89 ft + 8.14 ft = 13.03 ft traveled on the third bounce. The ball will then bounce again, but not rise high enough to count as a bounce, and come to rest. Adding up the distances traveled, we get 26 ft + 19.14 ft + 13.03 ft = 58.17 ft, which is closest to answer choice B, 75 ft.

A Tennis Ball Is Dropped from a Height of 15