A cannonball has a speed of 320 m/s at an altitude of 122 m above the ground. What is the total mechanical energy of the cannonball assuming that the potential energy at ground level is zero

Each kilogram of the cannonball has a total energy of 52396.454 joules.

Explanation:

From Principle of Energy Conservation we understand that energy cannot be destroyed nor created, but transformed. In this case non-conservative forces can be neglected, so that total energy of the cannonball () is the sum of gravitational potential () and translational kinetic energies (), all measured in joules. That is:

(Eq. 1)

By applying definitions of gravitational potential and translational kinetic energies, we proceed to expand the expression:

(Eq. 2)

Where:

- Mass of the cannonball, measured in kilograms.

- Gravitational acceleration, measured in meters per square second.

- Height of the cannonball above ground level, measured in meters.

- Speed of the cannonball, measured in meters per second.

As we do not know the mass of the cannonball, we must calculated the unit total energy (), measured in joules per kilogram, whose formula is found by dividing (Eq. 1) by the mass of the cannonball. Then:

If we know that , and , the unit total energy of the cannonball is:

Each kilogram of the cannonball has a total energy of 52396.454 joules.