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- May 13th 2009, 08:19 AMSarahGrBall drop and rebound question =/?
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- May 13th 2009, 08:41 AMartvandalay11
This is an infinite geometric series question with r=.8 and the coefficient equal to 12. Since r<1, this series converges and the ball actually travels a finite distance.

for |r|<1 that formula holds true, but in our case here, however I forgot that the ball bounces and falls so Soroban is correct - May 13th 2009, 08:53 AMSoroban
Hello, Sarah!

Quote:

A ball is dropped from a height of 12 feet.

The ball hits the ground and rebounds 80% of the distance it falls each time.

In theory, how far will the ball travel before coming to rest?

It falls 12 feet.

. . Then it falls that distance.

. . Then it falls that distance.

. . Then it falls that distance.

And so on . . .

We can see that the total distance is:

. .

. .

The geometric series has first term , common ratio

. . Its sum is: .

Therefore: .

- May 13th 2009, 10:36 AMSarahGr
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