Roregel: a ball rebounds one half the height from which it is dropped. the ball is dropped from a height of 160ft and keeps bouncing. what is the total vertical distance the ball will travel from the momement it is dropped to the momement it hits the floor for the fifth time?
You can approach the problem by computing it seperately for each bounce.
First the ball travels 160 ft
(hit the floor once)
the ball travels up 80 ft and down another 80 ft
So the total distance travelled is 160 + 80 + 80 = 320ft
(hit the floor twice)
the ball travels up 40 ft and down another 40 ft
So the total distance travelled is 160 + 80 + 80 + 40 + 40 = 320 + 40 + 40 = 400ft
(hit the floor three times)
the ball travels up 20 ft and down another 20 ft
So the total distance travelled is 160 + 80 + 80 + 40 + 40 + 20 + 20 = 400 + 20 + 20 = 440ft
(hit the floor four times)
the ball travels up 10 ft and down another 10 ft
So the total distance travelled is 160 + 80 + 80 + 40 + 40 + 20 + 20 + 10 + 10 = 440 + 10 + 10 = 460ft
(hit the floor five times)
Hence, the ball travels 460ft before it hits the floor five times.
+2353 
