### Brain Teasers

# Bouncy Ball

If you drop a bouncy ball from a distance of 9 feet from the floor, the ball will continue to bounce. Assume that each time it bounces back two thirds of the distance of the previous bounce. How far will the ball travel before it stops?

### Hint

Geometric series...### Answer

45 feet.The distance can be calculated as 9 + (9)*(2/3)*(2) + (9)*(2/3)*(2/3)*(2)+..., with the 2 accounting for the upward and downward travel distance. Adding 9 to this will result in the formation of an infinite geometric series: 18*(2/3)^0 + 18*(2/3)^1 +... Factoring out the 18 will result in a series that is equal to (1/(1-(2/3))), which equals 3. Multiplying by the 18 and then subtracting the nine used to create the series will result in 54 - 9 = 45.

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