An application of calculus: optimum parabolic path problem
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Abstract
A practical and technological application of calculus problem is posed to motivate freshman students or juniory high school students. Avariable coefficient of friction is used in modelling air friction. The case in which the coefficient of friction is a decreasing function of altitude is considered. The optimum parabolic path for a flying object for which the work done by variable coefficient air friction force is minimum is determined. If a flying object follows the determined path, energy requirement would be less compared with other parabolic or linear paths.