A simple solution for maximum range of projectile motion Available to Purchase

A fair amount of effort has been spent on the formulation of a simple, preferably noncalculus-based, solution for the maximum range,$Rmax$⁠, of the projectile fired with speed $R0$ from an elevation $y0$⁠. Here is a solution along the lines of the textbook treatment of the projectile motion.

If the projectile is fired from the point $(x0=0,y0)$ at an angle θ with respect to the x-axis, its trajectory is described by

With the observation that the projectile hits the ground at $y=0$⁠, the relation between the firing angle and the range of the projectile, $R=x(y=0)$⁠, is given by