Question 280869: A rubber ball dropped on a hard surface takes a sequence of vertical bounces. Each bounce is 1/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, What is the total distance it has traveled when it hits the surface the fifth time?
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! A rubber ball dropped on a hard surface takes a sequence of vertical bounces. Each bounce is 1/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, What is the total distance it has traveled when it hits the surface the fifth time?
It will be easier if we change  to the decimal 0.2
1. It falls 10 feet hitting the hard surface the first time.
That's 10 feet it has traveled when it hits the hard surface the first time.
2. It then bounces up 0.2 times 10, or 2 feet, and then falls 2 feet.
That's 4 more feet it has traveled, or a total of 10+4 or 14 feet when it hits
the hard surface the second time.
3. It then bounces up 0.2 times 2, or 0.4 ft, and then falls 0.4 ft. That's
0.8 ft more it has traveled, or a total of 14.8 feet when it hits the hard
surface the third time.
4. It then bounces up 0.2 times 0.4, or 0.08 ft, and then falls 0.08 ft.
That's 0.16 ft more it has traveled, or a total of 14.96 feet when it hits the
hard surface the fourth time.
5. It then bounces up 0.2 times 0.08, or 0.016 ft, and then falls 0.016 ft.
That's 0.032 ft more it has traveled, or a total of 14.992 feet when it hits
the hard surface the fifth time.
Answer: 14.992 feet.
Edwin
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