Meade, Douglas B. and Allan A. Struthers. 1999. Differential Equations in the New Millennium: The Parachute Problem. International Journal of Engineering Education. 15(6): 417-424.
Article Abstract: Introductory courses in differential equations have traditionally consisted of a long list of solution techniques for special equations. This characterization is becoming increasingly inaccurate as more textbooks and courses are being designed around qualitative methods. One component of many revised courses is the discussion of real-life applications and modeling. The parachute problem will be used to illustrate several essential features of the improved courses. In particular, it will be seen that the traditional version of the parachute problem is not very realistic, but is easily improved without making the problem significantly more complicated.
This paper builds a mathematical model for the various stages encountered by a skydiver with realistic modeling, data, and analysis. The assumptions are offered in a very realistic context, e.g., how long does one wait until pulling the chute cord when jumping from 4000 ft? The plots of the velocity and position over the various regimes within the jump are offered and discussed in context with what is actually happening.
Rarely seen in such pieces, we find an existence and uniqueness theorem for this differential equation and to apply theoretical techniques over each regime of the jump.
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