Rebound Superball Problem
The rebound ratio of a speckled green superball is 75%. It is dropped from a height of 16 feet. Consider the instant when the ball strikes the ground for the fiftieth time.
a. How far downward has the ball traveled at this instant?
b. How far ( upward and downward has the ball traveled at this instant?
c. How far would the ball travel if you just let it bounce...?
I have a feeling for the first two it would be something along the lines of "16(0.75)^0+16(0.75)^1...+16(0.75)^50", and for the second 2(" "), but there must be something that would allow me to do this calculation quicker than just adding 50 numbers together. Would it have something to do with ! ?