You don’t need much for the base, just a rod across the path of the arm that represents the stopping angle. The arm will be at the starting angle in the CAD. I expect you used a revolute joint at the axle of the arm. That can be a joint to ground, you don’t need a base.Â
Don’t use a constant velocity boundary condition for the reason you discovered. It just keeps going. Use a rotational (torsion) spring on the revolute joint with a preload and a spring rate. The preload torque will accelerate the arm from rest and the frictionless contact between the rod and the arm will stop the arm when contact is made, and the ball will keep going forward.
You can soften the deceleration of the arm and make the solution more likely to continue if you put a translational joint between the rod and ground, perpendicular to the arm at the point of contact. Then you can put a spring between ground and the rod. Adjust the mass of the rod and the spring rate to get the arm to decelerate at the rate that launches the ball nicely.