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Introduction
A recent homework problem that appeared in the forums was concerned with maximizing the horizontal range of a projectile subject to the launch site being a fixed height above the ground upon which the projectile eventually impacted. A number of interesting methods of solution arose so the idea of this article is to present all of these since each method illustrates a different approach to the problem and each is instructive in its own right.
The Problem
A cannon sits on top of a plane at a height ##h## above the ground and fires a shell with an initial velocity ##v_0##. At what angle ##\theta_0## must it fire the shell to attain maximum range ##R_{\text{max}}## along the ground?
I hope the OP (original poster) of the above problem will not mind me including his problem diagram:
Parametric Equations
The above motion may be represented by the following pair of...
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