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A ball is dropped vertically from a heig...

A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height d/2. Neglecting subsequent motion and air resistance, its velocity v varies with the heiht h above the ground as

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
A
a. Before hitting the ground, the velocity v is given by `v^2 = 2gd` (quadratic equation and hence
parabolic path)
Downward direction means negative velocity. After collision,
the direction become positive and velocity decreases.
Further, `v^2 = 2g xx (d/2) = gd, (v/v') = sqrt(2) or v = v'sqrt(2)`
As the direction is reversed and speed is decreased and hence
graph (a) represents these conditions correctly.
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