Q. A boy plays with a ball, and he drops if 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
(c) 6
(d) 7
Correct Answer: (b) 5
Question from UPSC Prelims 2021 CSAT Paper
Explanation :
A boy plays with a ball
Starting height = 1.5 meters
Bounce ratio = 4/5 (ball reaches 4/5th of previous height)
Stop condition = height < 0.5 meters (50 cm)
Height Calculations:
1. Initial Drop: 1.5 meters
2. First Bounce:
Height = 1.5 × 4/5 = 1.2 meters
3. Second Bounce:
Height = 1.2 × 4/5 = 0.96 meters
4. Third Bounce:
Height = 0.96 × 4/5 = 0.768 meters
5. Fourth Bounce:
Height = 0.768 × 4/5 = 0.6144 meters
6. Fifth Bounce:
Height = 0.6144 × 4/5 = 0.49152 meters
(This is less than 50 cm, so ball stops)
Result:
– Ball hits ground 5 times before stopping
– Final height (0.49152 m) is below stopping condition (0.5 m)
– Answer: 5 bounces
