JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Conservation of Momentum

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A ball is dropped from a height of 20 m. If the coefficient of restitution for the collision between ball and floor is 0.5, after hitting the floor, the ball rebounds to a height of ______ m.

Answer: 5

Solution

The coefficient of restitution for a bounce off a fixed floor links the rebound and drop heights through

e = \frac{h _{2}}{h _{1}}

, since the speeds just before and after impact are each set by

2 g h

. With

e = 0.5

and a drop height of

20 m

h_{2} = e^{2} h_{1} = (0.5)^{2} \times 20

. The ball climbs back to a height of

5 m

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Integer answer

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