Simple Model of a Standing Vertical Jump

TL;DR

This paper introduces a simple physics-based model of a standing vertical jump using Newton's laws, analyzing multi-segmented objects and comparing them to real jumpers for educational purposes.

Contribution

It presents the simplest model of a vertical jump based on Newton's laws and extends it to multi-segmented objects, highlighting pedagogical advantages.

Findings

Optimal number of segments for jumping identified

Model effectively illustrates basic physics principles

Comparison with real jumps discussed

Abstract

In this paper we use Newton's 3rd law to deduce the simplest model of an object that can perform a standing vertical jump -- a two-segmented object with an initial constant repulsive force between the segments, followed by an abrupt attractive force. Such an object, when placed on a sturdy ground, will jump, and the motion can be calculated using only the constant acceleration equations, making the example suitable for algebra-based physics. We then proceed to solve for the motion of an n-segmented object, and determine the optimal number of segments for jumping. We then discuss a few similarities and differences of this simple model from jumping robots and jumping humans, and then conclude by arguing the model's pedagogical merits.