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

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

Step-by-step 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+(1)/(2) gt^(2)`

`50=0+(1)/(2)(10)t^(2)`

`50=5t^(2)`

`10=t^(2)`

and
`t=√(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=(h)/(v)`

`t=(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`