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

Let us look at the kinetic and potential energies of an object of mass (m), falling freely from height (h), when the object is at different heights.

The point A is at a height (h) from the ground. Let the point B be at a distance V, vertically below A. Let the point C be on the ground directly below A and B. Let us calculate the energies of the object at A, B and C.

(1) Let the velocity of the object be v_B when it reaches point B, having fallen through a distance x.

(2) When the object is stationary at A, its initial velocity is u = 0

∴ K.E = 1/2 mass x velocity²

(3) Let the velocity of the object be vc when it reaches the ground, near point C.

From equations (i) and (iii) we see that the total potential energy of the object at its initial position is the same as the kinetic energy at the ground.