What Happens When a Ball Hits a Moving Wall?

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SUMMARY

When a ball is thrown towards a wall moving towards it, the outcome depends on the relative velocities involved. If a ball is thrown with velocity v towards a wall moving at speed w, in the wall's frame, the ball approaches at velocity v+w and rebounds at the same speed. Transitioning back to the lab frame, the ball's velocity becomes v+2w. In scenarios where w significantly exceeds v, the ball's final velocity approaches 2w.

PREREQUISITES
  • Understanding of basic physics concepts such as velocity and frames of reference.
  • Familiarity with kinematics and the principles of motion.
  • Knowledge of relative velocity calculations.
  • Basic grasp of Newtonian mechanics.
NEXT STEPS
  • Study the principles of relative velocity in different frames of reference.
  • Explore advanced kinematics problems involving moving objects.
  • Learn about the implications of momentum conservation in collisions.
  • Investigate real-world applications of these concepts in sports physics.
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Physics students, educators, and anyone interested in understanding motion dynamics and collision mechanics.

Domnu
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Problem
If you throw a ball with velocity [tex]v[/tex] at a wall, it rebounds with the same speed, [tex]v[/tex]. What happens if you throw it at speed [tex]v[/tex] towards a wall which is traveling towards you at speed [tex]w[/tex]? What is your answer in the limit in which [tex]w[/tex] is much larger than [tex]v[/tex]?

Answer
Let us work in the frame of the wall. The ball comes towards you at velocity [tex]v+w[/tex], so it must leave at velocity [tex]v+w[/tex] with respect to you. Moving back to the lab frame, this means that the ball moves now, to the left with velocity [tex]v+2w[/tex]. In the limit where [tex]w[/tex] is much larger than [tex]v[/tex], the velocity of the ball is [tex]2w[/tex].

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