A boy plays with a ball and he drops it from a height of 1 5 m Every time the ball hits the ground i...........

Math and Mental Ability Simplification

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?

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Explanation:

Given Height = 1.5 m = 1.5 × 100 cm = 150 cm
When ball hits the ground for the 1st time, its height = (4/5) × 150 = 120 cm
When ball hits the ground for the 2nd time, its height = (4/5) × 120 = 96 cm
When ball hits the ground for the 3rd time, its height = (4/5) × 96 = 76.8 cm
When ball hist the ground for the 4th time, its height = (4/5) × 76.8 = 61.44 cm
When ball hits the ground for the 5th time, its height = (4/5) × 61.44 = 49.15 cm
Since, it is given that if the previous height is less than 50 cm, the ball does not bounce further. So we
can say that after the ball hits the ground for the 6th time, it doesn’t bounce back.
Hence, option (3) is the correct answer.