Problem 12.

A man drops a 10 kg rock from the top of a ladder of height 5 m.

What is its speed just before it hits the ground?

What is its Kinetic Energy when it reaches the ground?

Solution:

In this problem we have free fall motion. We can solve this problem either by using the kinematics equations, which describe the motion with constant acceleration (free fall motion) or by using the energy conservation law.

Below we solve this problem by using the energy conservation law.

We assume that there is no friction, then we have the conservation of the net mechanical energy of the rock. The mechanical energy of the rock is a sum of the kinetic energy and gravitational potential energy:

The kinetic energy is determined by the speed of the rock:

The gravitational potential energy depends on the height of the rock:

Then the mechanical energy is

The conservation of the mechanical energy means that the mechanical energy in the initial state is equal to the mechanical energy in the final state:

or

.......................................(1)

The initial velocity is zero:

the initial height is 5 m:

the final height is zero (ground):

We do not know the final velocity:

We substitute these values in the equation (1) and obtain

Now we can find the final kinetic energy: