Answer:
d = 32*( 1 - 0.8^n) / 0.2 = 160*( 1 - 0.8^n)
Explanation:
Given:
- The initial height of the ball h_o = 32 ft
- The successive decrease in height after every bounce = 0.8*h
Find:
- The expression relating the total distance traveled by the ball for nth number of bounce.
Solution:
- The distance traveled by the ball upto n = 1, is = 32 ft
- The distance traveled by the ball upto n = 2, is = 32 + 2*32*.8 = 83.2
- The distance traveled by the ball upto n = 3, is = 83.2 + 2*32*.8*.8 = 124.16
- We can look for a pattern for the total distance traveled by geometric progression is as such:
d = a*( 1 - r^n) / ( 1 - r )
Where, r = 0.8 , and a = 32
d = 32*( 1 - 0.8^n) / 0.2 = 160*( 1 - 0.8^n)
Where, n = 1 , 2 , 3 , 4 , ......
