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A didactical exposition of the classical problem of the trajectorydetermination of a body, subject to the gravity in a resistant medium, isproposed. Our revisitation is aimed at showing a derivation of the problemsolution which should be as simple as possible from a technical point of view,in order to be grasped even by first-year undergraduates. A central role in ouranalysis is played by the so-called "chain rule" for derivatives, which issystematically used to remove the temporal variable from Newton's law to derivethe differential equation of the Cartesian representation of the trajectory,with a considerable reduction of the overall mathematical complexity. Inparticular, for a resistant medium exerting a force quadratic with respect tothe velocity our approach leads, in an elementary way, to the differentialequation of the trajectory, which is subsequently solved by series expansion. Acomparison of the polynomial approximants obtained by truncating such serieswith the solution recently proposed through a homotopy analysis is alsopresented.

Trajectory of a body in a resistant medium: an elementary derivation