A rubber ball is dropped from a height of 5 m onto a flat surface. Each time the ball hits the surface, it rebounds to 50% of its previous height. Find the total distance the ball travels.
A)5
B)10
C)20
D)15

Question

Quizplus · Accepted Answer

The total distance traveled by the ball includes both the distance it travels on the way down and the distance it travels on the way up after rebounding.

On the way down, the ball travels 5 meters.

On the way up, the ball travels 2.5 meters (50% of 5 meters).

Then, the ball again falls down from 2.5 meters and rebounds to 1.25 meters (50% of 2.5 meters), so the total distance traveled on the way up is 2.5 + 1.25 = 3.75 meters.

Therefore, the total distance traveled by the ball is 5 + 3.75 = 8.75 meters. But we need to consider the distance traveled by the ball both on the way down and the way up after each rebound. In total, the ball hits the surface 3 times (from the initial drop and two rebounds), so we need to double the distance traveled to get the total distance.

Therefore, the total distance traveled by the ball is 8.75 x 2 = 17.5 m, which is closest to choice D (15).

A Rubber Ball Is Dropped from a Height of 5