Since the iron cylinder is not magnetic, all the solenoid will do is attract it. It would take some pretty clever timing to collapse the magnetic field when the cylinder was moving at the desired speed so that it turned into a projectile and carried out through the far side of the solenoid. Not saying it's impossible, but it doesn't seem very easy to me. Is it important that the cylinder itself is the projectile? If you use the solenoid as an impulse driver to throw something else, the problem gets much easier.