A 100-kg cart is 10 meters off the ground on a roller coaster track. How far up will it go on the other side before it stops and falls back down again?

In this scenario, the cart at a height of 10 meters possesses gravitational potential energy due to its elevation above the ground. As it descends the track, this potential energy is converted into kinetic energy, allowing the cart to move. When the cart reaches the lowest point, it will have maximum kinetic energy.

As it climbs the other side of the track, the cart converts kinetic energy back into gravitational potential energy. Assuming there is no loss of energy to friction or air resistance, the potential energy at the peak of the ascent would equal the initial potential energy when it was at 10 meters.

Since the energy conversion is ideally without losses, the maximum height the cart can reach on the opposite side is the same as its initial height, which is 10 meters. Therefore, when the cart stops and falls back down, it will reach the peak height of 10 meters before reversing direction. This is why the answer indicating that the cart rises 10 meters on the other side is correct.