What kind of evidence supports that a child swinging can predict future motions?

The choice indicating that the consistent height a child reaches during each swing cycle is the correct answer because it directly relates to the principles of energy conservation and the predictable behavior of swinging motions. When a child swings, the motion follows a pattern governed by gravitational potential energy and kinetic energy. As the swing rises to a certain height, all the energy is potential, and as it moves downward, that potential energy is converted into kinetic energy. The consistent height achieved indicates that energy transformations are stable and predictable for the swing's motion, allowing one to predict future positions of the swing based on its cycle.

In contrast, while the speed at which the child swings, the potential energy stored in the swing position, and the child’s weight do influence the dynamics of swinging, they do not inherently provide the same level of predictability regarding future motions as the consistent height achieved does. The height reached is a definitive indication of the energy dynamics engaged in the swing's motion, allowing observers to anticipate how far and how high the swing will go in the next cycle.