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Putnam 1940 B1

Source: Putnam 1940

February 22, 2022
Putnamtrigonometryphysics

Problem Statement

A projectile, thrown with initial velocity v0v_0 in a direction making angle α\alpha with the horizontal, is acted on by no force except gravity. Find the lenght of its path until it strikes a horizontal plane through the starting point. Show that the flight is longest when sin⁡αlog⁡(sec⁡α+tan⁡α)=1.\sin \alpha \log(\sec \alpha+ \tan \alpha)=1.
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