A 30 N rock falls from a 40 m cliff. At what point during its fall are its potential and kinetic energies equal?

Both energies are equal when the rock has fallen 20 m or equivalently when it is at a height of 20 m.

Explanation:

Potential and Kinetic Energy

The gravitational potential energy is the energy an object has due to its height above the ground. The formula is

Where:

m = mass of the object

g = acceleration of gravity (9.8~m/s^2)

h = height

Note we can also use the object's weight W=mg into the formula:

The kinetic energy is the energy an object has due to its speed:

Where v is the object's speed.

Initially, the object has no kinetic energy because it's assumed at rest.

The W=30 N rock falls from a height of h=40 m, thus:

Since the sum of the kinetic and potential energies is constant:

U' + K' = 1,200 J

Here, U' and K' are the energies at any point of the motion. Since both must be the same:

U' = K' = 600 J

U'=Wh'=600

Solving for h':

Both energies are equal when the rock has fallen 20 m or equivalently when it is at a height of 20 m.