Question

On a day when the velocity of sound is 340 m/s, a boy drops a stone from the top of a high tower. If the tower is 50 m tall, how long will it take for the boy to hear the returning sound?

Answer 1

Answer:

It takes 3.31 s for the boy to hear the returning sound of the stone

Explanation:

Ok, the time after which splash is heard is equal to the time acquired by the stone to reach the ground + time taken by sound to return.

First, u=0 m/s (this is the initial speed with which the stone was thrown), h=50 m (is the height of the tower) and g=10 m/$s^{2}$ (is the gravity)

We can use this equation that relates the free fall of the object:

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

$50=0+\frac{1}{2}(10)t^{2}$

$50=5t^{2}$

$10=t^{2}$

and $t=\sqrt{10}=3.16 s$

t =3.16 s is the time it takes the stone to fall

Second, h=50 m and v=340 m/s (that it's the speed of sound)

We can use this equation:

$h=vt$

$t=\frac{h}{v}$

$t=\frac{50}{340}=0,15 s$

t=0.15 is the time it takes for the sound to return

Finally, both times are added, obtaining the time in which the boy will hear the returning sound of the stone:

$t= 3.16 s + 0.15s$$=3.31 s$