Question

How does an infinite geometric series apply to being pushed on a swing?

Answer 1

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 `6/7` of its previous swing. The total horizontal distance can be expressed as the geometric series:

`3+3(6/7)+3(6/7)^2+3(6/7)^3+cdots=3/{1-6/7}=21`

In theory, the total horizontal distance is `21` m.

I hope that this was helpful.