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.
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
Starting with a height of