How far can Tarzan jump?

(color online) Schematic view of the Tarzan swing motion. Tarzan initially stands on the platform (A). He swings from this point and reaches the swing nadir  (B), from where he swings ahead to the launching point (C), where he releases the rope to achieve as long a flight distance as possible to reach the landing site (D). All the variables and constants used in the present article are displayed.

Hiroyuki Shima
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.
Read more: http://arxiv.org/pdf/1208.4355v1.pdf

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