How does an infinite geometric series apply to being pushed on a swing?
If you wish to find the total horizontal distance traveled by you on a swing after a big initial push assuming that the amplitude of each swing decreases at a fixed rate. We can think of the total distance as the sum of a geometric series.
Assume that the initial push gives you a 3 m swing and that a swing is
In theory, the total horizontal distance is
I hope that this was helpful.