Question 1081203: A rubber ball is dropped in front a height of 27 meters. Each time that it hits the ground it bounces to a height 2/3 od the time from which it fell. Find the distance that it travels up to the time that it hits the ground for the 5th time. The total distance travelled by the ball until it comes to rest.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! distance is a/(1-r), where r=2/3
First was up 18, then 12 then 8 then then 16/3 after coming up for the fourth time. Then it hits the ground for the fifth time
That sum is 43 1/3 m distance it travels up.
The sum of the series converges to 81
27+18+12+8+16/3...
BUT, the distance traveled by the ball is
27+18+18+12+12+8+8+...
That is 27 + 54(2), since the rest of the values converge to the total sum of 81, but it is going up and down.
The total distance is 135 m.
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