Question

A stone is dropped into a lake by a person from a 500 m high tower. He would hear the sound of after approximately. (a) 10 s (b) 11.5 s (c) 14 s (d) 21 s

Answer 1

$\large\underline{\underline{\sf Given:}}$

• Height of tower (s) = 500m

$\large\underline{\underline{\sf To\:Find:}}$

• Time of hearing sound of water splash $\sf{(t_1)}$=?

$\large\underline{\underline{\sf Solution:}}$

According to third equation of motion :

$\large{\boxed{\sf s=ut+\frac{1}{2}at^2}}$

Initial Velocity (u) = 0

a = g = 10m/s²

$\large\implies{\sf 500=0+\frac{1}{2}×10×t^2}$

$\large\implies{\sf t^2=100}$

$\large\implies{\sf t=\sqrt{100} }$

$\large\implies{\sf t=10\:s }$

Remember :

${\boxed{\sf Velocity\:of\:sound\:in\:air=332m/s}}$

•°• time of sound travel = $\sf{(t_1-10)s}$

We know ,

$\large{\boxed{\sf Distance=Sound×Time }}$

$\large\implies{\sf 500=332×(t_1-10) }$

$\large\implies{\sf t_1=\dfrac{500}{332}+10 }$

$\large\implies{\sf t_1=11.5\:s}$

$\Large\underline{\underline{\sf Answer}}$

•°•$\large\underline{\underline{\sf Time\:of\:hearing\:water\:splash}}$

$\large\underline{\underline{\sf is\:11.5\:s}}$