Question

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.

Accepted Answer

Step 1: Begin by identifying the key phases of the tennis ball's motion: (1) free fall from the third-story balcony, (2) collision with the sidewalk, and (3) upward motion after the bounce until it reaches the maximum height near the second story. Step 2: For the free fall phase, note that the ball is accelerating downward due to gravity. Represent this in the motion diagram with velocity vectors increasing in length as the ball approaches the sidewalk. The acceleration vector (gravity) points downward throughout this phase. Step 3: At the lowest point (the collision with the sidewalk), the ball experiences a rapid change in velocity due to the force exerted by the sidewalk. The acceleration at this point is upward and much larger in magnitude than gravity, as it reverses the ball's direction. Indicate this with a short upward acceleration vector at the lowest point in the motion diagram. Step 4: For the upward motion after the bounce, the ball slows down as it rises due to gravity acting downward. Represent this in the motion diagram with velocity vectors decreasing in length as the ball approaches its maximum height. The acceleration vector (gravity) continues to point downward throughout this phase. Step 5: At the maximum height of the bounce (near the second story), the ball's velocity is momentarily zero before it begins to fall again. Indicate this in the motion diagram with no velocity vector at the peak and a downward acceleration vector due to gravity.

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Acceleration at the Lowest Point