A ball is thrown straight up. At what point does the ball have the most energy? Ignore air resistance.

1. At the highest point of its path.
2. When it is first thrown.
3. Just before it hits the ground.
4. When the ball is halfway to the highest point of its path.
5. Everywhere; the energy of the ball is the same at all of these points.

In the absence of any non-conservative force such as friction or air resistance, the total mechanical energy of a system remains constant.

It is given by the formula:

\(\begin{aligned}P{E_{\rm{i}}} + K{E_{\rm{i}}} &= P{E_{\rm{f}}} + K{E_{\rm{f}}}\\mg{h_{\rm{i}}} + \frac{1}{2}mv_{\rm{i}}^2 &= mg{h_{\rm{f}}} + \frac{1}{2}mv_{\rm{f}}^2\end{aligned}\)

The potential energy is zero, and the kinetic energy is the maximum at the bottom. As the ball rises, the kinetic energy gets converted into gravitational potential energy. At the top, the potential energy is the maximum, and the kinetic energy is zero.

The mechanical energy remains constant throughout the motion. The ball will have the same (maximum) energy at all points.