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⁻¹.

Answer 1

Height of the stone h = 500 m, g = 10 ms⁻²

Initial speed of the stone u = 0

Time taken by the stone to reach the surface of water from the top of the tower = t₁

∴ h (= S) = ut₁ + `1/2"gt"_1^2`

500 m = `0 xx "t"_1 + 1/2 xx 10 xx "t"_1^2` 

⇒ 500 = `5 xx "t"_1^2`

⇒ `"t"_1^2 = 500/5`

⇒ `"t"_1^2` = 100

⇒ t₁ = `sqrt100`

= 10 s

Total time taken by sound to reach the top of the tower after splash heard = t₂

∴ t₂ = `"Distance"/"Speed"`

= `h/V`

= `500/340`

= 1.47 s

Total time taken by sound to reach the top of the tower after splash heard

t = t₁ + t₂ 

= 10 + 1.47

= 11.47 s¹