math
posted by long nguyen .
a student drop a rubber ball from a height of 8 feet . Each time the ball hits the ground, it bounces to 75% of its previous height.
a/ how far does the ball travel between tne second and third bounces .
b/ write an infinite series to model the total distance tralveled by the ball, excluding the distance traveled before the firstbounce

we have to count the up and the down of each bounce
So from the moment of the first bounce:
distance = 2(.75)(8) + 2(.75^2)(8) + 2(.75^3)(8) + ...
= 16(.75) + 16(.75^2) + 16(.75^3) + ...
so we have a GS, with
a = 16 ,r = .75
distance between 3rd and 2nd
= 16(.75^2)  16(.75^3) = 2.25 ft
total distance = a/(1r) = 16/(1.75) = 64 ft