Final answer:
The ball-earth system has the most potential energy and no kinetic energy at the top of the path; the total energy remains constant along the trajectory. The statement about having most kinetic energy at the top is incorrect, as kinetic energy is zero at that point. Throughout the ball's motion, potential energy and kinetic energy interchange while their total sum remains constant.
Step-by-step explanation:
Considering a ball tossed directly upward in the context of a ball-earth system, there are key principles related to energy that come into play. According to the law of conservation of energy, the total energy of the system remains constant throughout the motion of the ball.
At the top of the path, the ball has the most potential energy and its kinetic energy is zero because its velocity is zero at that instant. It does not have the most kinetic energy at the top, that statement is incorrect. The most kinetic energy is present when the ball is moving fastest, which is right before it leaves the hand and right before it is caught again (ignoring air resistance).
The total energy of the system does not change as the ball moves along its trajectory, assuming there is no air resistance or other external forces doing work on the system. The kinetic energy and potential energy can transform into each other as the ball rises and falls, but their sum remains constant. This concept is referred to as mechanical energy conservation.