Question

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

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

Answer 1

The correct option is B 8.7 s

First, we find the time taken by the stone to reach the base of the tower.

We use the relation,

$s=ut+\frac{1}{2}a{t}^2$ ......(1)

Here,

Distance, $s=300m$

Initial velocity, $u=0$

Putting these values in formula (1),

Acceleration due to gravity, $g=9.8m/s^2$

$300=0+\frac{1}{2}\times 9.8\times t^2$

$t^2=\frac{300}{4.9}=61.224$

$t=7.82s$

Time taken by sound to travel from base of the tower to its top,

$t^{\prime }=\frac{Distance}{Speedofsound}=\frac{300}{340}=0.882s$

Total time after which the splash is heard $=t+t^{\prime }=7.82+0.882=8.7s$