The floating-arm trebuchet is a more energy-efficient modern variant of the medieval trebuchet that had received little treatment in literature. In this project, I improve an already-existing Lagrangian mathematical model of the floating-arm trebuchet and combine it with a numerical analysis of projectile motion with air resistance to predict the relationship between the hook angle and the range of the projectile. To compare the theory to reality, I built my own small-scale floating-arm trebuchet and tested it with multiple values of hook angle. Similar trends were observed showing that the Lagrangian model is relatively accurate at predicting the behaviour of the floating arm trebuchet but that it could be improved in the future by taking into account the effect of friction.