A tennis ball strikes a perfectly vertical wall

PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

A tennis ball strikes a perfectly vertical wall. Immediately before impact the ball’s velocity components are vx=+15 m s−1v_x = +15\,\text{m}\,\text{s}^{-1} (to the right, toward the wall) and vy=−5.0 m s−1v_y = -5.0\,\text{m}\,\text{s}^{-1} (downward). After the very brief collision, the xx–component of the ball’s velocity reverses sign but keeps the same magnitude, while the yy–component is unchanged. Ignore gravity and spin during the collision. (a) Sketch and label the momentum vector of the ball just before and just after the collision. (b) Based on your sketch, describe qualitatively the direction of the impulse delivered to the ball by the wall. (c) Explain, using the impulse–momentum theorem, why the wall can reverse only the horizontal component of the ball’s momentum but not the vertical component during this interaction. (d) If the time of contact is decreased while all other conditions remain the same, describe how the magnitude of the average force exerted by the wall on the ball would change and justify your answer.

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