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 = 10 m//s^2` and speed of sound `= 340 m//s`.

Answer 1

Distance covered by stone, `s = 500 m`
Initial speed, `u = 0`
And, Time taken, `t = ?` (To be calculated)
And, Acceleration, `g = 10 ms^(-2)`
Now, `s = ut + (1)/(2) g t^(2)`
`500 = 0 xx t +(1)/(2) xx 10 xx t^(2)`
`500 = 5 xx t^(2)`
`t^(2) = (500)/(5)`
`t^(2) = 100`
`t = sqrt(100)`
Time, `t = 10 s` ....(1)
Thus, the stone takes 10 seconds to fall into pond of water and produce the sound of splash. This sound of splash has to travel a distance of 500 m to be heard at the top of the tower.
Now, speed of sound `= ("Distance travelled by sound")/("Time taken by sound")`
So, `340 = (500)/("Time taken by sound")`
And, Time taken by sound `= (500)/(340)s`
`= 1.47 s` ....(2)
Time after which splash is `= 10 s + 1.47s`
heard at the top of tower `= 11.47s`