2008 AMC 8 Problems/Problem 12
Problem
A ball is dropped from a height of meters. On its first bounce it rises to a height of
meters. It keeps falling and bouncing to
of the height it reached in the previous bounce. On which bounce will it not rise to a height of
meters?
Solution
Each bounce is 2/3 times the height of the previous bounce the first bounce reaches 2 meters, the second 4/3 the third 8/9 the fourth 16/27 and the fifth 32/81 Half of 81 is 40.5 so the ball does not reach the required height on bounce C:5
See Also
2008 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.