SOLUTION: A rubber ball dropped on a hard surface takes a sequence of bounces, each on 2/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, what is the total v

Algebra ->  Sequences-and-series -> SOLUTION: A rubber ball dropped on a hard surface takes a sequence of bounces, each on 2/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, what is the total v      Log On


   

Question 853282: A rubber ball dropped on a hard surface takes a sequence of bounces, each on 2/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, what is the total vertical distance it has traveled after it hits the surface the fifth time? Be sure to account for both drop and rebound differences.
a - 22 12/25feet
b - 32 124/125feet
c - 25 124/125feet
d - 22 124/125feet
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
The ball falls first from 10 feet
then rises again
Number of falls = number of rises + 10 feet
It is a geometric series
a= 4
r= 2/5
n= 4
Sn = %28a1%281-r%5En%29%29%2F%281-r%29
Substitute the values
we get Sn = 6 49/99
Distance during rises
Distance during falls = 6 49/99 + 10 = 16 49/99
Total = 6 49/99 + 16 49/99 = 22 98/99
Option (d)