Resistance Is Not Futile: Air Resistance in an Algebra-Based Course

Abstract

In this paper we show that an object's terminal speed due to air resistance depends not on any of the object's details, but only on the distance at which an object reaches a particular fraction of its terminal speed. We show this graphically and algebraically. Although a mathematical treatment of air resistance is beyond the scope of an algebra-based, introductory physics course, some of the concepts involved are important for (at least) three reasons. First, the equations used for uniform acceleration only approximately (and perhaps badly!) describe projectiles students know (a home-run baseball, for example). With the equation for terminal speed, students can estimate the speeds at which the simple kinematic equations no longer produce “reasonable” approximations.