Maple and the parachute problem: Modeling with an impact

The ''parachute problem'' involves a first-order ODE in which the coefficient of air resistance is a piecewise-defined function. This paper focuses on the use of Maple's symbolic, numeric, and graphic tools to facilitate the analysis of this initial value problem. Of particular interest is a qualitative analysis of the solution. The form of the problem most commonly found in textbooks is shown to be physically unrealistic. An improved model is proposed and analyzed. The paper concludes with the analysis of parameter sensitivity of the model and the solution of an interesting control problem. The graphical analysis is based on two Maple procedures, motion and plot motion which are defined in this paper.