Consider a rubber ball freely falling from a height h = 4.9 m onto a… | JEE Main 2009 (AIEEE)

Q51JEE Main 2009 · AIEEEMedium

Motion Under Gravity

Consider a rubber ball freely falling from a height $h = 4.9\text{ m}$ 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 and the height as a function of time will be:

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Answer: (b)

Upward positive: falling, $v$ goes linearly from 0 to $-v_1$ in time $t_1$ .
Elastic bounce: $v$ jumps from $-v_1$ to $+v_1$ at once.
Then $v$ falls linearly (slope $-g$ ) from $+v_1$ through 0 at $2t_1$ to $-v_1$ at $3t_1$ , and repeats.
Height: parabolic arcs, each returning to the same height $h$ .
So the answer is (b).

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Motion Under Gravity question from JEE Main 2009 (AIEEE)

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