Question

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

• A. $5.6s$
• B. $8.7s$
• C. $9.7s$
• D. $4.7s$

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 taken by the stone to fall down $\left(t_1\right)$ and the time taken by the sound to travel from bottom to top $\left(t_2\right)$ .

Given:
Initial velocity, $u=0m{s}^{-1}$
Height of the tower, $s=300m$
Acceleration due to gravity, $g=9.8m{s}^{-2}$
Velocity of sound, $v=340m{s}^{-1}$

Finding $t_1$:
Using second equation of motion,
$s=ut+\frac{1}{2}a{t}^2$
$s=\frac{1}{2}g{t}_1^2$
$t_1=\sqrt{\frac{2s}{g}}$
$t_1=\sqrt{\frac{2\times 300}{9.8}}$
$t_1\approx 7.82s$

Finding $t_2$:
From definition of speed:
$Speed=\frac{Distance}{Time}$
$t_2=\frac{300}{340}$
$t_2\approx 0.88s$

Hence, total time is:
$t=t_1+t_2$
$t=(7.82+0.88)s=8.7s$