Your roommate drops a tennis ball from a third-story balcony. It hits the sidewalk and bounces as high as the second story. Draw a complete motion diagram of the tennis ball from the time it is released until it reaches the maximum height on its bounce. Be sure to determine and show the acceleration at the lowest point.

Verified step by step guidance

1. Identify the key points in the motion of the tennis ball: the release point, the point of impact with the sidewalk, and the highest point of the bounce.
2. Draw a vertical line representing the path of the tennis ball. Mark the release point at the top (third-story balcony), the impact point at the bottom (sidewalk), and the highest point of the bounce (second-story height).
3. Indicate the direction of motion of the tennis ball. It moves downward from the release to the impact point, and then upward from the impact point to the highest point of the bounce.
4. At each point, draw vectors to represent the velocity of the tennis ball. The velocity vectors point downward before the ball hits the sidewalk and upward as it rises to the highest point of the bounce. The magnitude of the velocity vector is greatest at the impact point and decreases to zero at the highest point of the bounce.
5. At the lowest point (sidewalk), draw a vector to represent the acceleration due to gravity, which points downward. This acceleration remains constant throughout the motion, but is especially important at the lowest point where the change in direction and speed is most abrupt.

Key Concepts

Free Fall

Free fall refers to the motion of an object under the influence of gravity alone, with no other forces acting on it. In this scenario, the tennis ball accelerates downward at approximately 9.81 m/s² until it hits the ground. This concept is crucial for understanding the ball's motion as it falls from the balcony.

Elastic Collision

An elastic collision occurs when two objects collide and bounce off each other without losing kinetic energy. In the case of the tennis ball, when it hits the sidewalk, it undergoes an elastic collision, allowing it to bounce back to a height corresponding to the second story. This concept helps explain the ball's behavior after impact.

Acceleration

Acceleration is the rate of change of velocity of an object. At the lowest point of the ball's trajectory, just before it bounces, the acceleration is still due to gravity, acting downward. Understanding acceleration is essential for analyzing the forces acting on the ball during its fall and bounce.