When a ball bounces, it rises to $\frac{3}{4}$ of the height from which it fell. If the ball is dropped from a height of 32 m, how high will it rise at the third bounce?
(a)13 m
(b)$13 \frac{1}{2} \mathrm{m}$
(c)$14 \frac{1}{2} \mathrm{m}$
(d)None of these
Answer
Answer (as printed): B
Explanation
Height at the third bounce $=\left[32 \times\left(\frac{3}{4}\right)^{3}\right] \mathrm{m}=\left(32 \times \frac{27}{64}\right) \mathrm{m}$ $$=\frac{27}{2} \mathrm{m}=13 \frac{1}{2} \mathrm{m} .$$