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I'm mostly lost as to how the hell to even begin this equation. This is the first projectile motion problem I've had where I actually need to find the derivative of something. The maximum hight is not going to be 2R, because that makes the distance farther, and thus the velocity increases. The distance can not be too close either because then the angle increases and requires a larger velocity.

With this many unknowns, i'm a bit lost. What I think I need to do is find a relation of the radius to this odd parabola of my projectile motion. So I'm looking at it like a geometry problem.

Any hints are appreciated!