Problem of the Week 1222

A T-Shirt Gun

The stands at a stadium slope up at an 18° angle. You are firing a T-shirt cannon from the bottom of the stands into the stands.

At what angle of elevation above the ground should you fire the cannon to get the shirt to land as far up the stands as possible? Ignore air resistance.

This can be solved by fairly standard calculus methods. I have a hunch there is an elegant way to solve this that does not invoke calculus — one where the angle 18° is replaced by an arbitrary angle A — but I do not know such a solution. I say this because the answer is a very simple formula in A.

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March 2016