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A ball is dropped from 100 feet. Every time it hits the ground, it rebounds to 1/3 of its previous height. Find the total distance the ball travels.

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Answer:

200'

Explanation:

There's probably a formula for it, but you can work it out pretty easily with a little simple math (if all they want is a number):

It falls 100'.

It bounces up 33.3' feet, then falls that same distance: 66.6' on this trip.

It bounces up 11.1', then drops: 22.2' this trip

It bounces up 3.7': 7.4' this trip

It bounces up 1.23': 2.5' total

It bounces up 0.4': 0.8' total

It bounces up 0.14': 0.3' total

It bounces up 0.05: 0.1' total

Then it's pretty much done.

So add them up:

100 + 66.6 + 22.2 + 7.4 + 2.5 + 0.8 + 0.3 + 0.1 = 199.9'

Call it 200' (the last few little bounces supply the missing 0.1'.)

They may want an equation, but they should appreciate your (my) perseverance if you submit it this way.

User Timrael
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