If a ball is dropped from a height of 10 meters, and on each bounce it reaches a maximal height of 0.75 times the previous height, then what is the total distance traveled? If we use as the maximal height reached on bounce , as the initial height, and as the factor of the maximal height achieved relative to the previous bounce, we have .
Then, the total distance traveled is:
Using if , we get:
Now we plug our values of and into this equation to find meters. So, even though our ball will bounce on for eternity, it will travel exactly 70 meters!