A special rubber ball is dropped from the top of a wall that is 512 feet high. Each time the ball bounces, it rises half as high as the distance it fell. The ball is caught when it bounces 1 foot high. How many times did the ball bounce?
A) 256
B) 10
C) 18
D) 9
E) 512

Question

A special rubber ball is dropped from the top of a wall that is 512 feet high. Each time the ball bounces, it rises half as high as the distance it fell. The ball is caught when it bounces 1 foot high. How many times did the ball bounce? ​
A) 256
B) 10
C) 18
D) 9
E) 512

Quizplus · Accepted Answer

Each time the ball bounces, it rises half as high as the distance it fell. So, after the first bounce, it reaches 256 feet (half of 512) and falls back down to 256 feet. After the second bounce, it reaches 128 feet (half of 256) and falls back down to 128 feet. Continuing this pattern, we get:

1st bounce: 512 feet
2nd bounce: 256 feet
3rd bounce: 128 feet
4th bounce: 64 feet
5th bounce: 32 feet
6th bounce: 16 feet
7th bounce: 8 feet
8th bounce: 4 feet
9th bounce: 2 feet
10th bounce: 1 foot

Therefore, the ball bounces 9 times. Answer choice D is correct.

A Special Rubber Ball Is Dropped from the Top of a Wall