A rubber ball is dropped from height 10 meters. If it rebounds aprox 1/2 the distance after each fall, use geometric series to aprox the total distance that the ball travels before coming to rest.
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Let's baby-talk our way through this . . .A rubber ball is dropped from height 10 meters.
If it rebounds aprox 1/2 the distance after each fall, use geometric series
to approximate the total distance that the ball travels before coming to rest.
The ball falls 10 meters: .
It bounces up 5 meters and falls 5 meters: .
It bounces up meters and falls meters: .
It bounces up meters and falls meters: .
It bounces up meters and falls meters: .
. . and so on . . .
The total distance is: .
.[1]
The geometric series has: .first term , common ratio
. . Its sum is: .
Substitute into [1]: . meters.