I've built a horizontal spring launcher, and i need to calculate the extension needed in the spring in order to launch a projectile horizontally to a given distance. The launcher consists of a striker connected to the spring... when the spring is pulled back and let go the strike moves forward and hit the projectile. i have the vertical distance of the launch, the mass of both the launcher system (mass of spring + mass of striker), mass of the projectile, the distance the projectile needs to travel and also the spring constant (k), so far... i have: Kinetic Energy (launcher) + Elastic Potential Energy = Kinetic Energy (projectile) problem i run into... is that i can't simplify the equation ... i get to: Mlauncher*Vlauncher^2 + k*x^2 = Mprojectile*Vprojectile^2 Vprojectile = deltaX / time time = SquareRoot[DeltaY/(g/2)] g = 9.8m/s^2 Vlauncher = (Mprojectile * Vprojectile) / Mlauncher i need to make an equation that allows me to solve for x (spring extension).... but i just can't simplify it properly.... If anyone could help me out, it would be greatly appreciated. Thanks. By the way, is there a general formula to calibrate something like this?