Alead ball is dropped into a lake from a diving board 5.0 meters above the water. after entering the water, it sinks to the bottom with a constant velocity equal to the velocity with which it hit the water. the ball reaches the bottom 3.0 seconds after it is released. how deep is the lake?

28.8 meters

Explanation:

We must first determine at which velocity the ball hits the water. To do so we will:

1) Assume no air resistance.

2) Use the Law of conservation of mechanical energy: E=K+P

Where

E is the mechanical energy (which is constant)

K is the kinetic energy.

P is the potential energy.

With this we have

Where:

m is the balls's mass <- we will see that it cancels out and as such we don't need to know it.

v is the speed when it hits the water.

g is the gravitational constant (we will assume g=9.8.

h is the height from which the ball fell.

Because when we initially drop the ball, all its energy is potential (and ) and when it hits the water, all its energy is kinetic (. And all that potential was converted to kinetic energy.

Now, from we can deduce that

Therefore v=9.6

Now, to answer how deep is the lake we just need to multiply that speed by the time it took the ball to reach the bottom.

So D=9.6*3=28.8

Which is our answer.

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