Lets say i am using a counterweight and a weight on the other end of an arm (that i want to launch like a trebuchet)- im not sure how to find the formula between the range of motion and the weight (and angle of launch): this is what i tried-
$$Ek=Ep \text{(energy converted from potential to kinetic of weight)}$$ $$\frac{mv^2}{2}=mgh, v= \sqrt{2gh}$$
Then i used $Range= v^2\frac{\sin(2\theta)}{g}$ to find range but i keep getting really weird answers- where am i going wrong with this please?