Question

A stone is dropped into a lake from a tower 500 m high. The sound of the splash will be heard by a man on the tower after :

[Assume speed of sound = 330 m/s; g = 10 m/s${}^2$]

• A. 21 s
• B. 10 s
• C. 11.5 s
• D. 14 s

Answer 1

The correct option is C 11.5 s

Height of the tower $S=500$ m

Initial speed of the stone $u=0$

Acceleration due to gravity acting on the stone $g=10m/s^2$

Using $S=u{t}_1+\frac{1}{2}g{t}_1^2$

where $t_1$ is the time taken by the stone to reach the lake.

$\therefore$ $500=0+\frac{1}{2}\left(10\right)t_1^2$

We get $t_1=10$ s

Speed of sound in air $v=330m/s$

Time taken by the sound of splash to reach the top of tower $t_2=\frac{S}{v}$

$\therefore$ $t_2=\frac{500}{330}=1.5$ s

Thus total time after which the sound of splash will be heard $t=t_1+t_2$

$\therefore$ $t=10+1.5=11.5$ s