Question

Prove that the kinetic energy of a freely falling object on reaching the ground is nothing but the transformation of its initial potential energy.

Answer 1

Total energy at initial position = K.E + P.E = 0 + mgh

Total energy when it reaches the ground = K.E + P.E = 0.5mv^2 + 0

Velocity when it reaches the ground = sqrt(2gh)
Substitute velocity in total energy equation


Total energy when it reaches the ground = 0.5mv^2 = 0.5m * 2gh = mgh

We found that total energy when it reaches the ground = Total energy at initial position.

In other words, kinetic energy with which it hits the ground is the transformation of its initial potential energy.