Question

A stone is dropped into a pond from the top of the tower of height h. If n is the speed of sound in air, then the sound of splash will be heard at the top of the tower after a time

• A. $\sqrt{\frac{2h}{g}} + \frac{h}{v}$
• B. $\sqrt{\frac{2h}{g}} - \frac{h}{v}$
• C. $\sqrt{\frac{2h}{g}}$
• D. $\sqrt{\frac{2h}{g}} + \frac{2h}{v}$

Answer 1

Answer: (A)

$\sqrt{\frac{2h}{g}} + \frac{h}{v}$

Answer 2

Let $t_{1}$ be the time taken by the stone to strike the surface of water in the pond.

Using $h = ut + \frac{1}{2}gt^{2}$

$\therefore H = \frac{1}{2}gt_{1}^{2}$ $(\because u = 0)$

Or $t_{1} = \sqrt{\frac{2h}{g}}$

Time taken by sound to reach the top of tower, $t_{2} = \frac{h}{v}$Total time after which splash of sound is heard

$t = t_{1} + t_{2} = \sqrt{\frac{2h}{g}} + \frac{h}{v}$