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Geometric series

  • Thread starter apiwowar
  • Start date
  • #1
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a ball is dropped from a height of 10 feet, each bounce is 3/4 of the height of the bounce before

a)find an expression for the height hn to which the ball rises after it hits the floor for the nth time

so hn= 10(3/4)n

b) find an expression for the vertical distance Di the ball has traveled when it hits the floor for the first, second, third, and fourth times.

im a little confused on this part, how would Di relate to hh? or do they even relate at all?

would it be 10 + 10(3/4)n since after it hits the ground the first time it will decrease by 3/4 of the previous height each time?

c) find an expression for the total vertical distance the ball has travelled when it hits the floor for the nth time

im sure once figure out b this will make perfect sense

any hints or tips on how to do this would really be appreciated.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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The first time it hits the floor it's travelled 10*(3/4)^0=10 feet. The second time it's travelled 10*(3/4)^0+2*10*(3/4)^1. The '2' is because it goes up and down. The third, 10*(3/4)^0+2*10*(3/4)^1+2*10*(3/4)^2. Etc. For the first few times you can just add it up by hand. For the nth time you have to sum the geometric series.
 

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