On the rise and fall of a ball with linear or quadratic drag

Abstract

We review the problem of a vertically thrown ball, with a drag force which is either linear or quadratic in the speed. It is stressed from the outset that these two types of drag correspond to specific ranges of the Reynolds number (Re<1 and 103<Re<2×105, respectively) and do not hold outside these intervals. We also include the buoyant force in our treatment of the problem. The equations of motion are solved analytically and several true-to-life examples are discussed. The calculations are somewhat harder than for the well-known case without drag force, but no highbrow mathematics is required and the extra effort is amply compensated by the gain in realism and surprise value. © 1999 American Association of Physics Teachers