Question

A stone dropped from the top of a tower of height 300 m splashes into a pond of water at its base. When will the sound of the splash be heard at the top?
(Velocity of sound = $340m{s}^{-1}$ and g = 9.8 $m{s}^{-2}$)

• A. 5.6s
• B. 8.7s
• C. 5.4s
• D. 6.7s

Answer 1

The correct option is B

8.7s

Time after which the splash is heard at the top is equal to the sum of the time $t_1$ taken by the stone to fall down and the time $t_2$ taken by the sound to travel from bottom to top.
Height = 300 m, hence s = 300m.
$g=9.8m{s}^{-2}$
$u=0$ (Stone is dropped, not thrown)
$t_1=?$
Using $s=u{t}_1+\frac{1}{2}a{t_1}^2$
We get, $s=\frac{1}{2}g{t_1}^2$
$t_1=\sqrt{\frac{2s}{g}}=\sqrt{\frac{2\times 300}{9.8}}$
$\Rightarrow t_1$ = 7.82 s
Again $t_2$ = height of tower/velocity of sound.
$t_2=\frac{300}{340}=0.882s$
Total time $=t_1+t_2=(7.82+0.88)s=8.7s$