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Question
A ball is dropped from a height of 10m. It bounces to a height of 6m, then 3.6m and so on. Find the total distance travelled by the ball
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Solution
Here, on the first bounce, the ball will go 6 m and it will return 6 m.
On second bounce, the ball will go 3.6 m and it will return 3.6 m, and so on and so forth….
∴ Total distance travelled by the ball is
= 10 + 2[6 + 3.6 + ...]
The terms 6, 3.6 …. are in G.P.
∴ a = 6, r = 0.6
Since, |r| = |0.6| < 1
∴ sum to infinity exists.
∴ Total distance travelled by the ball
`= 10 + 2 [6/(1 - 6/10)]`
`= 10 + 2[6/((10 - 6)/10)]`
`= 10 + 2[(6 xx 10)/4]`
= 10 + 30
= 40 m
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