The black box is some sort of trebuchet design that has an efficiency of 100%. We cannot study the motion before release, since we don't know how it works, so we'll study the motion after release. The trebuchet has an initial potential energy given by PE=Mcwgh. Since no energy is lost, the initial kinetic energy of the projectile is given by KEproj=1/2Mprojv2. The range for a given velocity, released at an angle q above the horizontal, is given by the equation R=(2v2sinqcosq)/g. Then the maximum range is Rmax=v2/g. The range can also be expressed as Rmax=2(Mcw/Mproj)h. The range efficiency of the treb can be determined by dividing the range of the throw by the maximum range for the counterwieght height. Or, eR=2RhMproj/Mcw.