Calculating Initial Speed of Projectile Given Starting Height, Horizontal Distance, and Launch Angle

A trebuchet similar to those used in the Punkin' Chunkin' contest is looked at, and from estimates of the height it was launched from, the angle it was released at, and the horizontal distance it travels before striking the ground, the initial launch speed is calculated. This involves setting up two equations and two unknowns and using substitution to solve for the answer.