Abstract
This article concerns the problem of maximizing the horizontal range of a projectile that is launched from atop a tower and is subject only to gravity and linear air resistance. Here the surface to which the projectile is launched is represented by a continuous function whose intersection with every flight path is a single point. In this general setting, tools from real analysis need to be employed to gain detailed information about the shape of the graph and the maximum of the distance function. In particular, the article provides geometric insight into the maximal lateral displacement of the projectile and the corresponding optimal launch angle.
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Kantrowitz, R., Neumann, M.M. Optimization of projectile motion under linear air resistance. Rend. Circ. Mat. Palermo 64, 365–382 (2015). https://doi.org/10.1007/s12215-015-0205-y
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DOI: https://doi.org/10.1007/s12215-015-0205-y