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Newton was sitting on a tree from there he vertically throws a tennis ball, which consistently bounces back 3/5 of the height from which it is dropped. What fraction of its original height will the ball bounce after being dropped and bounced 3 times without being stopped?

Newton was sitting on a tree from there he vertically throws a tennis ball, which consistently bounces back 3/5 of the height from which it is dropped. What fraction of its original height will the ball bounce after being dropped and bounced 3 times without being stopped? Correct Answer 27/125

Given∶

A tennis ball is consistently bounces back 3/5 of the height from which it is dropped.

Formula Used∶

Geometric progression, Concept of Decreasing GP.

GP whose common ratio r lies between 0 and 1.

Calculation∶ 

Each time the ball is dropped and it bounce back, it reaches 3/5 of the height it was dropped from.

After the first bounce, the ball will reach 3/5 of the height from which it was dropped. Let it was the original height.

After the second bounce, the ball will reach 3/5 of the height it would have reached after the first bounce.

So, at the end of the second bounce, the ball would have reached 3/5 × 3/5 of the original height = 9/25th of the original height.

After the third and the last bounce, the ball will reach 3/5 of the height it would have reached after the 2nd bounce.

So, at the end of the last bounce, the ball would have reached 3/5 × 3/5 × 3/5 of the original height = 27/125 of the original height.

∴ The required fraction is 27/125 of its original height.

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