a rubber ball is dropped from the top of a hole. Exactly 0.5 seconds later, the sound of the rubber ball hitting bottom is heard. How deep is the hole?

Question

how deep is the hole

Answer 1

Hi Lindsey

 

Let D = Depth

is given by

D = 1/2 gt²

 

let this time be t_{1 =} sqrt 2D_/ g

 

let t₂ = time taken by sound to travel up

 

t₂ = D/ speed of sound = D /340

 

Total time = t₁ +t₂ =0.5 sec

 

2D/9.8 = 0.5*0.5 + D²/( 340*340) - 2 *0.5*D /340

 

Solve it for D

 It could be simple equation if time taken by sound is ignored and only t_¹ needs to be calculated but the Depth will be just over 1m