In the scetch shown the trebuchet is released by dropping the counterweight $($marked Mc$).$The beam rotates about the fulcrum $($F$)$which is placed $2\mathrm{.}5$meters to the left of the rightmost end of the beam. Teh beam is assumed to be uniform density. The length of the beam is exactly $10$meters$.$ The sling hanging from the end of the beam can be assumed to be weightless and rotates freely about the endpoint of the beam. It has a spherical payload mass at the end of $($Mp$,$Payload mass$).$The payload is released when the tangential velocity of the payload makes a $45$degree angle with the ground as shown in the diagram. Given the following information, write an equation or set of equations to predict the distance the payload will travel from the point it is released $($ignore the height of the trebuchet and the distance of the sling for the distance traveled calculation$).$The three varying parameters within the equation are as follows. The mass of the counterweight $($Mc$)$The mass of the payload $($Mp$)$and the length of the sling $($Ls$).$Assume no parts "bump into one another or the ground"