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A rubber ball is dropped from a height of 5m on a plane, where the acceleration due to gravity is not shown. On bouncing it rises to 1.8m. The ball loses its velocity on bouncing by a factor of

1. 16/25
2. 2/5
3. 3/5
4. 9/25

Correct answer: 3/5

Solution

The velocity of the ball just before hitting the ground is proportional to the square root of the height it falls from, and the velocity after bouncing is proportional to the square root of the height it rises to. The ratio of velocities is √(1.8/5) = 3/5, so the ball loses its velocity by a factor of 3/5.

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