Hello my dear Sherlocks and Einsteins, I hope you have your puzzle hats on, and maybe your math brain working.
This week’s puzzle might include a bit of math, so if that’s not your thing, you can skip to the answer in the comments!
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This puzzle may require a certain amount of thought.
Imagine that you have a pair of perfectly elastic balls, one very much larger and heaver than the other. You place the lighter ball on top of the heavier one, and then drop them a distance of 1ft onto a perfectly rigid floor.
How high will the lighter ball bounce?
It may help to bear in mind that kinetic energy is: (mass x (speed x speed)) / 2.
As always, answers are in the comments!
ANSWER BELOW
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9ft. Just before impact, the balls are traveling at an unknown speed pf X meters per second. Since the balls are perfectly elastic and the floor perfectly rigid, the heavy ball will hit and its speed go from x (downward) to -x (upward).
In that instant, the light ball will suddenly be traveling a a speed of 2x compared to the heavy ball, since x is two more than -x.
It reflects from the heavy ball, traveling at -2x compared to it – and since the heavy ball is moving at -x already, the light ball is then moving at -3x compared to the floor.
Since its energy is dependent on its speed squared, however much energy it gained in falling, it now possesses nine times that energy to rise with.
So it will climb to 9x1ft, or 9ft.
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