How do you measure vertical velocity? Assuming I have zero horizontal velocity, I can achieve a 45 degree take-off angle using your equation which is not possible under any known mechanical system in this universe or dimension. Or is it your equation should read vv + hv = 90 degrees? Then what about impulse and what role does that play? How about that horizontal velocity and velocity are not governed by the same force constraints although some do overlap like viscosity of muscles.
My equation?! I was only stating the obvious, 45 degree take-off angle is produced when vertical and horizontal velocity, at the instant of take-off, is equal.