Question

A stone is dropped from the top of a tower $500$m high into a pond of water at the base of the tower. When is the splash heard at the top ? (Given $g=10m{s}^{-2}$ and speed of sound =$340m{s}^{-1}$)

• A. $10s$
• B. $11.47s$
• C. $1.10s$
• D. $20s$

Answer 1

The correct option is B $11.47s$

Given - $h=500m,g10m/s^2,v=340m/s$ ,

by , $h=ut+\left(1/2\right)g{t}^2$ ,

$500=0+\left(1/2\right)10t^2$ , (initial velocity , $u=0$) ,

or $t^2=1000/10=100$ ,

or $t=10s$ ,

it is the time taken by stone to reach the water level , after that a sound is produced due to strike of stone on water , and sound travels upwards .Let t' be the time taken by sound to reach the base of tower ,

then , $t^{\prime }=h/v=500/340=1.47s$ ,

therefore time taken by splash to hear at the top ,

$T=t+t^{\prime }=10+1.47=11.47s$