Difference between revisions of "2008 AMC 8 Problems/Problem 12"
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==Solution== | ==Solution== | ||
| − | Each bounce is | + | 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== | ==See Also== | ||
{{AMC8 box|year=2008|num-b=11|num-a=13}} | {{AMC8 box|year=2008|num-b=11|num-a=13}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 16:18, 8 August 2021
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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
