A ball is dropped from rest from height h above the ground in frame S (the Earth's frame). Another frame S^\prime is moving upwards with constant speed u relative to the Earth. In frame S^\prime, the ball has initial downward speed v. Pertaining to the change in kinetic energy (\Delta K) of the ball from release to just before hitting the ground as measured in frames S and S^\prime separately, which one of the following is correct?

  1. A. \Delta K is the same in both the frames.
  2. B. \Delta K is larger in frame S.
  3. C. \Delta K is larger in frame S^\prime. ✓
  4. D. \Delta K cannot be compared without the information of mass of the ball.

Correct Answer: C. \Delta K is larger in frame S^\prime.

Explanation

In frame S, \Delta K = \frac{1}{2}m(v_f^2 - 0) = mgh. In frame S^\prime, initial speed is u and final speed is \sqrt{2gh} + u. \Delta K^\prime = \frac{1}{2}m((\sqrt{2gh}+u)^2 - u^2) = mgh + mu\sqrt{2gh}. Therefore, \Delta K^\prime is larger.

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