Simple model of a standing vertical jump

Abstract

In this paper we use Newton’s third law to deduce the simplest model of a system 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 conclude by arguing the model’s pedagogical merits.