Prove that the mechanical energy of a freely falling object in the gravitational field remains constant at every point.

In the figure, the height of the building is h and let the object be at a height x above the ground level.

1: The total energy(E) of the object when it was at the top of the building was potential energy(U)

E = U = mgh

2: The total energy of the object when at a height of x above the ground level is partly kinetic energy (K) and potential energy.

The velocity v of the object is gien by,

As the initial energy is 0,

So,

Now the potential energy is

U = mgx

Hence, the total energy of the object is

E = K + U = mg(h-x) + mgx

E = mgh

Hence, it is proved that the mechanical energy of freely falling on object in gravitational the eld remain constant remains point as x is any arbitrary distance.