Some Transcendental Results Concerning Air Resistance

When a projectile is shot or a ball is thrown, the simplest mathematical model ignores air resistance and obtains the familiar parabolic path of motion (see [2] for example). When air resistance is taken into account, the motion is more complicated, and the flight time satisfies a transcendental equation ([I], [3], [4]). The nature of the equation depends on the form of velocity dependence assumed for the drag force. The simplest form, that of linearty, is approximately correct for low to moderate speeds (cf. [I]), but at higher speeds the drag force is approximately proportional to the square of the speed (cf. [3]). In this article we assume linearity, i.e., a drag force directly proportional to speed (Stokes'sLaw).