I've been working on this for a while, with little luck. We are told that an object is on a cliff of height H, and is launched off with a velocity v at an angle of theta with the vertical. gravitational acceleration is g. To get the maximum range, it must be a certain angle theta, given by the formula: cos^2(θ)=(v^2)/(2v^2+2gh). Prove that this is correct. v*sin=range/t, -h=v*cos*T-.5gT^2, getting a quadtratic theorem, and deriving. No luck, I get ugly giant equations rather than that small solution.