The magnetic force on the ball changes as the ball moves through the magnetic field. In order to calculate what the total work done on the ball is (and thus its kinetic energy and from that its momentum), you will need to use calculus.

Fortunately, as a college student now, calculus is probably the first college-level math class you will take, if you haven't already at the end of high school. If you haven't been exposed to calculus yet and are anxious to get started right now, I suggest you check out the Wikipedia article on "derivative" and work through the examples. There are ALL KINDS of cool things you can do with derivatives (e.g. ever wondered WHY the one-half part of the distance-acceleration formula is there? Velocity is the derivative of acceleration, and position is the derivative of velocity...). If you HAVE been exposed to calculus already, then the thing you need to do to get the work done on the metal ball is to integrate the force over the distance traveled. Once you have the kinetic energy, you can get the velocity, and from that, the momentum (assuming of course you know the mass of the ball, which you also need).