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.
A) 16
B) 24
C) 8
D) 32

Question

Quizplus · Accepted Answer

When the ball is dropped from a height of $8 \mathrm{~m}$, it first travels down $8 \mathrm{~m}$ and then hits the surface. After the first bounce, it reaches a height of $\frac{1}{2} \times 8 \mathrm{~m} = 4 \mathrm{~m}$. It then falls back down another $4 \mathrm{~m}$ and bounces up to a height of $\frac{1}{2} \times 4 \mathrm{~m} = 2 \mathrm{~m}$. After the second bounce, it falls back down another $2 \mathrm{~m}$ and bounces up to a height of $\frac{1}{2} \times 2 \mathrm{~m} = 1 \mathrm{~m}$. After the third bounce, it falls back down another $1 \mathrm{~m}$ and bounces up to a height of $\frac{1}{2} \times 1 \mathrm{~m} = 0.5 \mathrm{~m}$.

At this point, the ball has traveled a total distance of $8 + 8 + 4 + 4 + 2 + 2 + 1 + 1 + 0.5 + 0.5 = 32 \mathrm{~m}$. However, the final bounce only takes the ball to a height of $0.5 \mathrm{~m}$, so it does not travel any further. Therefore, the total distance the ball travels is $32 \mathrm{~m}$ and the answer is (B).

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