# 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 : **

## Bouncing Ball – Boys Plays with Ball

This is a question about a geometric sequence. The ball is dropped from a height of 1.5 m and bounces back to attain a height 4/5th of the previous height each time it hits the ground. The ball stops bouncing when the previous height is less than 50 cm.

Let’s calculate the height of each bounce:

- First bounce: 1.5 * (4/5) = 1.2 m
- Second bounce: 1.2 * (4/5) = 0.96 m
- Third bounce: 0.96 * (4/5) = 0.768 m
- Fourth bounce: 0.768 * (4/5) = 0.6144 m
- Fifth bounce: 0.6144 * (4/5) = 0.49152 m

The fifth bounce is less than 50 cm, so the ball will stop bouncing after hitting the ground for the fifth time.

So the correct answer to this question is (b) 5.