The ball's motion is periodic because it undergoes an elastic collision with the ground, conserving mechanical energy and allowing it to return to the initial height with each bounce, following a predictable cycle.
Step-by-step explanation:
When a ball is dropped from a height of 4 meters and makes an elastic collision with the ground, it will rebound to the same height assuming no mechanical energy is lost to air resistance or other factors. In this situation, the motion of the ball is periodic because it follows a predictable and repeating path: dropping from the initial height, colliding with the ground, and returning to the initial height, over and over again.
This periodic motion can be described by the same principles that govern simple harmonic motion, although the scenario with the ball bouncing is not a perfect example of simple harmonic motion. The key aspect that makes the motion periodic is the conservation of mechanical energy during each cycle of its movement. Because the collisions are elastic, the potential energy at the initial height is converted to kinetic energy just before the collision and then converted back to the same amount of potential energy at the maximum height after the bounce. This process repeats indefinitely, or until an outside force or source of energy loss alters the system.