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I'm trying to design a formula that determines the launch velocity, launch angle, and time spent in the air for a projectile if only the initial launch height, maximum height reached, and total horizontal distance traveled before the projectile hits the ground are known. It's not too hard to design a formula if the initial height is the ground (since the parabolic path taken by the projectile is symmetrical), but once the initial height and ground level are different, things get a lot harder. I tried looking everywhere online and deriving my own formula, without success. Does anyone know of such a formula?

Thanks,

Matt