The best graph would show potential energy starting high and decreasing as the cannonball rises, while kinetic energy increases as the cannonball falls, with both energies equating to a constant total mechanical energy throughout the flight, demonstrating conservation of energy.
The graph that best represents the relationship between the potential energy and the kinetic energy of a cannonball as it flies over the bow of a ship and falls onto the beach is one where potential energy is highest at the launch and decreases as the cannonball rises, whereas kinetic energy is zero at the highest point of flight and is maximum just before impact. At any point during the cannonball's trajectory, the addition of potential and kinetic energies equals the total mechanical energy of the system, assuming no air resistance and no energy loss. Initially, all energy is potential (at the top of the flight), which converts to kinetic as the cannonball falls, peaking just before impact on the beach.
During the cannonball's ascent, kinetic energy is transformed into potential energy, and during its descent, potential energy is converted back into kinetic energy. At the peak of the flight, potential energy is at its maximum, and kinetic energy is at a minimum. Conversely, when the cannonball hits the beach, kinetic energy is at its maximum because the cannonball is moving fastest just before impact, and potential energy is minimal.
Through the process, the sum of potential energy and kinetic energy remains constant, showcasing the conservation of energy principle in physics.