A lead ball is droped into a lake from a diving board 5m above the water . It hits the water with a certain velocity and then sink with constant velocity in bot

Question

A lead ball is dropped into a lake from a diving board 5m above the water . It hits the water with a certain velocity and then sink with constant velocity in bottom . It reaches the bottom 5 second after it is dropped If g= 10m/s² . Find depth of the lake and average velocity of the ball ? 

Answer 1

The initial time, to reach the water can be calculated:

S=Vi*t + 0.5gt²

Vi=0

S=5m

t=1 sec to touch the water

Velocity when it touches the water is

Vf²=Vi+2g*S

Vi=0

S= 5m

Vf= √(2gh)= 10 m/sec

I will have to assume that the speed that the ball has in the water is the same constant that it reached the lake surface, there is no buoyancy effect or friction.

then the ball will sink during 4 secs at a speed of 70.7 m/sec

the lake is 4X 10= 40 m deep

The average speed will be in the water 100m/sec

The average speed in all the run will be

45/5 = 9 m/sec