What is the distance between your hand and the surface water? What is the speed of sound in this case?

Question

While stationary on a boat you are measuring the time it takes for the coin to leave your hand and hit the water. In order to measure that time you are turned to the sound of the coin hitting the water. You know that it takes 5.5 seconds for the coin to leave your hand and hit the water but the timer that you are using shows 6 seconds. 

Answer 1

Distance between hand and water:

 

If you ignore air resistance, and the coin starts from rest,

 

y = (1/2) g t^2 =(1/2) (9.8 m/s^2) (5.5 s)^2 = 148.225 m

 

But it took an extra half second for the sound to travel the distance y and reach you.  So speed of sound is:

 

v = y / (delta t) = (148.225 m) / (0.5 s) = 296.45 m/s