Understanding the Concepts

* Potential Energy (PE): Energy stored due to an object's position relative to a reference point (usually the ground).

* Kinetic Energy (KE): Energy possessed by an object due to its motion.

* Conservation of Mechanical Energy: In the absence of non-conservative forces (like friction or air resistance), the total mechanical energy (PE + KE) of a system remains constant.

Solution

1. Initial Total Energy: The initial total energy of the ball is the sum of its potential and kinetic energy:

* Total Energy (Initial) = PE + KE = 100 J + 700 J = 800 J

2. At the Top of the Trajectory: At the very top of its trajectory, the ball momentarily stops moving. This means its kinetic energy is zero (KE = 0). Since mechanical energy is conserved, the total energy at the top must still be 800 J.

3. Potential Energy at the Top: Since the ball has no kinetic energy at the top, all its total energy is now potential energy:

* Potential Energy (Top) = Total Energy (Initial) = 800 J

Therefore, the ball's potential energy at the top of its trajectory is 800 J.