Write the equation of total mechanical energy of a body of mass $m$ falling freely from a height $H$.

(N/A) The total mechanical energy $(E)$ of a body is the sum of its kinetic energy $(K)$ and potential energy $(U)$.
For a body of mass $m$ falling freely from a height $H$,at any height $h$ (where $0 \le h \le H$),the velocity $v$ of the body is given by the equation of motion $v^2 = u^2 + 2g(H-h)$. Since the body falls from rest,$u = 0$,so $v^2 = 2g(H-h)$.
The kinetic energy is $K = \frac{1}{2}mv^2 = \frac{1}{2}m(2g(H-h)) = mg(H-h)$.
The potential energy at height $h$ is $U = mgh$.
The total mechanical energy is $E = K + U = mg(H-h) + mgh = mgH - mgh + mgh = mgH$.
Thus,the equation for total mechanical energy is $E = mgH$.