anonymous
  • anonymous
A ball is dropped from a height of 10 m. It rebounds 1/2 the distance on each bounce. What is the total distance the ball travels? (Round your answer to the nearest whole number)
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
this can be seen as a geometric series with a starting term of 10, and a common ratio of 1/2
anonymous
  • anonymous
S=u1/(1-r) =10/(1-1/2) =10/0.5 =20
anonymous
  • anonymous
20m using the formula for geometric infinite series

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anonymous
  • anonymous
so the \[Sum _{\infty} = \frac{10}{1 - \frac{1}{2}}\] which is 20

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