You stuck like in a spring then cut the rope and energy is trasmitted to the body on the catapult. Then this body just have a parabolic motion on a X-Y plane that follows
##x=x_0+v_(0x)t,y=y_0+v_(0y)t-g/2t^2##
Check out this very cool website that details how a catapult works
http://www.real-world-physics-problems.com/catapult-physics.html
