The Maximum Velocity of a Falling Body

摘要

An earlier article on Falling Humans in Mathematics Today [1] made for a very interesting read, along with other earlier letters [2, 3], because it put much needed meat on the bones of what I would call a motion resistance factor associated with travel through the upper atmospheres. It was triggered by the great fall of Felix Baumgartner. In one of the letters an 'exponential decay with height' model was employed to represent, in effect, the motion resistance factor and the purpose of this note is to examine further this type ot model, lo show how it relates maximum velocity to height. Specifically, the motion resistance factor can be represented by a simple two-parameter exponential model that permits a closed form solution to the equation of motion. This solution can be exploited to determine values for the two parameters that are required to support known facts. In this fashion it is possible to replicate some of the results/curves in the literature above. This model, simple as it is, is instructive and shows how a mathematical artefact can be employed to describe the motion of a falling body that reaches a maximum velocity at some intermediate flight point, after which it slows down.