Question

A ball is dropped from a height of 12 feet and returns to a height that is one-half of the height from which it fell. How far will the ball have traveled when it hits the ground for the fourth time?. . A. 12 feet. . B. 24 feet. . C. 3 feet. . D. 33 feet¥

Answer 1

Answer: (D) 33 feet

First consider that the height is 12 feet and the ball is dropped from that height and the ball bounces back up to half the height that is 6 feet, then second time when the ball is dropped, according to the given question, the height becomes 6 feet and when the ball returns back then it returns back to half of the height that is 3 feet, following the similar path, we can write bounces one at a time:

1.  Ball is dropped from 12 feet and bounces back to 6 feet.

2. Ball is dropped from 6 feet and bounces back to 3 feet.

3. Ball is dropped from 3 feet and bounces back to 1.5 feet.

4. Ball is dropped from 1.5 feet and reaches the ground.

Adding the total distance traveled,we get

12+6+6+3+3+1.5+1.5=33 feet.

Answer 2

The best thing to do in order to calculate the distance of the ball taht would have traveled when it hits the ground for the fourth time is to list the height everytime it bounces. We calculate as follows:

12+6+6+3+3+1.5+1.5 = 33 feet