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A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to 81/100 of the height through which it falls. Find the average speed of the ball. [Take g = 10 m s⁻²]

1. 3.0 m s⁻¹
2. 3.50 m s⁻¹
3. 2.0 m s⁻¹
4. 2.50 m s⁻¹

Correct answer: 2.50 m s⁻¹

Solution

The average speed of the ball can be calculated by considering the total distance traveled during its bounces and the total time taken. Since the ball bounces to a height of 4.05 m after the first drop and continues to rise to 81% of the previous height, the total distance is a geometric series, and the time can be derived from the heights using the formula for free fall. The resulting average speed comes out to be 2.50 m/s.

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