Question

A stone is dropped from the top of a tower of $500\text{m}$ height, into a pond of water at the base of the tower. When is the splash heard at the top?

$(\text{Given}g=10{\text{ms}}^{-2}$ and speed of sound $=340{\text{ms}}^{-1})$

• A. $10\text{s}$
• B. $11.47\text{s}$
• C. $1.10\text{s}$
• D. $20\text{s}$

Answer 1

The correct option is B $11.47\text{s}$

Given $h=500\text{m},g=10{\text{m/s}}^2,v=340\text{m/s},$
Since the stone is under free fall, we can use the kinematic formula, $h=\frac{1}{2}g{t}^2$.
From the data given in the question,

$500=\frac{1}{2}\times 10\times t^2$
$\Rightarrow t^2=1000/10\Rightarrow t=10\text{s}$

It is the time taken by stone to reach the water level. After that, sound is produced due to the stone striking the water surface, and the sound travels upwards.

Let $t^{\prime }$ be the time taken by the sound to reach the top of the tower.
Then, $t^{\prime }=\frac{h}{v}=\frac{500}{340}=1.47\text{s}$

Therefore, total time taken for the splash to heard at the top,
$T=t+t^{\prime }=10+1.47=11.47\text{s}$

Thus, option (b) is the correct answer.