Suppose a ball is dropped from a height of 16 feet. each time it drops h feet, it rebounds 0.81h feet. find the total distance traveled by the ball. round your answer to two decimal places

When the ball is first dropped, it falls feet. On the first bounce, it rebounds feet, which means on the second "drop" it must travel feet again. On the second bounce, the ball rebounds feet, and on the third drop falls the same distance. And so on.

So there are two directions to track:




The total distance is the sum of these two:



Recall that for an infinite geometric sum, you have



provided that . So the total distance traveled by the ball is



Starting with a height of means the total distance is about 152.42 ft.

It equals 1373.5 that’s the solution