SOLUTION: A ball dropped from a height of 100 m and after each fall, it rebounds 1/3 of the distance from which it fell. Find the total distance travelled by the ball before coming to re

Algebra ->  Sequences-and-series -> SOLUTION: A ball dropped from a height of 100 m and after each fall, it rebounds 1/3 of the distance from which it fell. Find the total distance travelled by the ball before coming to re      Log On


   



Question 1188229: A ball dropped from a height of 100 m and after each fall, it rebounds 1/3 of the
distance from which it fell. Find the total distance travelled by the ball before
coming to rest.
I honestly cannot figure out how to write the working equation for it. Please help, thank you!

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let the total distance travelled by the ball before coming to rest be d
d+=+100+%2B+2%2A100%2A%281%2F3%29 [the factor 2 is for equal distance being covered up and down after each bounce of the ball]
d+=+100+%2B+2%2A100%2A%281%2F3%29}*(sum of an infinite GP series whose 1st term is 1 and common ratio is 1%2F3)
d+=+100+%2B+2%2A100%2A%281%2F3%29%2A%281%2F%281+-+1%2F3%29%29
d+=+100+%2B+2%2A100%2A%281%2F3%29%2A%283%2F2%29+
d=+200m