How far can Tarzan jump?

Abstract

The tree-based rope swing is a popular recreation facility, often installed in outdoor areas, giving pleasure to thrill-seekers. In the setting, one drops down from a high platform, hanging from a rope, then swings at a great speed like "Tarzan", and finally jumps ahead to land on the ground. The question now arises: How far can Tarzan jump by the swing? In this article, I present an introductory analysis of the Tarzan swing mechanics, a big pendulum-like swing with Tarzan himself attached as weight. The analysis enables determination of how farther forward Tarzan can jump using a given swing apparatus. The discussion is based on elementary mechanics and, therefore, expected to provide rich opportunities for investigations using analytic and numerical methods.