Aball 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¥

(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.