Consider a rubber ball freely falling from a height h=4.9m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time the height as function of time will be
(A)(see structures)AB
(B)(see structures)AB
(C)(see structures)AB✓ Correct
(D)(see structures)AB
Answer: (C)
Solution
While the ball falls its speed grows uniformly as v=gt, and the perfectly elastic bounce reverses the velocity instantly without any loss, so the speed then falls back to zero on the way up and the pattern repeats; a graph of velocity against time is therefore a straight-line sawtooth that flips sign at each bounce. The height meanwhile follows h=21gt2 downward and an identical parabola upward, so it traces a series of equal parabolic arcs returning to the same maximum each time. The correct choice is the pair showing this sawtooth velocity together with the repeating parabolic height.
JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option