A rubber ball is dropped from a height of $8 \mathrm {~m}$ 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. Select the correct answer.
A) 16
B) 24
C) 8
D) 32

Question

Quizplus · Accepted Answer

The distance traveled by the ball in each rebound is equal to the distance it travels from its rebound height to the surface, plus the distance it falls from its maximum height to its rebound height.

At each rebound, the distance traveled is:
\begin{align*}
& 8 	ext{ m (falling)} + 4 	ext{ m (rising)} \
= & 12 	ext{ m}
\end{align*}

The total distance traveled is the sum of the distances traveled during each rebound, plus the distance it fell from its initial height before the first rebound:
\begin{align*}
& 8 	ext{ m (initial fall)} + (2 	imes 12 	ext{ m}) \
= & 32 	ext{ m}
\end{align*}

Therefore, the correct answer is B) 24.

A Rubber Ball Is Dropped from a Height Of 8 m8 \mathrm {~m}8 m

A Rubber Ball Is Dropped from a Height Of $8 \mathrm {~m}$