Which of the following illustrates a pattern that can predict future motion?

The choice illustrating a pattern that can predict future motion is the scenario of a child swinging on a swing. This situation involves a recurring motion that can be described by periodicity. When a child swings, they follow a predictable back-and-forth motion, governed by the principles of physics such as gravity and pendulum motion.

This predictability is particularly evident because the swing's motion can be modeled mathematically. Factors such as the height from which the child starts swinging, the length of the swing, and gravitational force determine the swing's period (the time it takes for one complete cycle of motion). This repeatable behavior allows observers to anticipate how far and how high the swing will go on subsequent swings, based on initial conditions.

In contrast, a rock placed on a hill, a still water surface, and a parked car do not demonstrate ongoing motion or a predictable pattern of movement. The rock could potentially move if it is disturbed, but this is not a predictable motion without further context. A still water surface represents a state of equilibrium without motion, and a parked car is simply at rest, lacking any aspect of predictable motion. Thus, the swinging child exemplifies the only option where motion can be clearly analyzed and predicted over time.