A boy plays with a ball and he drops it from a height of 1·5 m. Every time the ball hits the ground, it bounces back to attain a height 4/5th of the previous height. The ball does not bounce further if the previous height is less than 50 cm. What is the number of times the ball hits the ground before the ball stops bouncing ?
- (a) 4
- (b) 5 ✓ UPSC's answer
- (c) 6
- (d) 7
Why the answer is (b)
• The ball is dropped from 1.5 m, which is 150 cm, and it hits the ground for the 1st time from 150 cm.
• After each hit, the next bounce height is 4/5 of the previous height: 120 cm, 96 cm, 76.8 cm, 61.44 cm, and 49.152 cm.
• The ball hits the ground from 150 cm (1st), 120 cm (2nd), 96 cm (3rd), 76.8 cm (4th), and 61.44 cm (5th).
• After the 5th hit, the next bounce height is 49.152 cm, which is less than 50 cm, so the ball does not bounce further.
• Therefore, the ball hits the ground 5 times before stopping, so option (b) is correct.
Why the other options are wrong
- (a) 4
- Option (a) is wrong because it stops counting after the 4th hit, but the ball still hits the ground a 5th time from 61.44 cm before the next bounce height falls below 50 cm.
- (c) 6
- Option (c) is wrong because it adds a 6th hit, but after the 5th hit the ball reaches only 49.152 cm, which is less than 50 cm, so no 6th hit occurs.
- (d) 7
- Option (d) is wrong because it adds two extra hits, but the bounce height falls below 50 cm after the 5th hit, so no 6th or 7th hit occurs.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.