# Where could you go in a 20km iron asteroid?

We know from this question that an asteroid 20 km in diameter is feasible as a hollow space habitat.

There are many variables in real life, but assuming you had a spherical solid iron asteroid 20 km in diameter orbiting the Solar system in the Kuiper belt. When you start hollowing it out to form your habitat, you use a coilgun or railgun to impart thrust. Now you potentially have an interstellar ship.

Assuming you have decided to leave an outer shell 1 km thick, this gives you 18 km diameter sphere of iron as reaction mass. Assuming we could eject this mass with the velocity of 0.1 c, and the rate of ejection at 10 k tons per hour, what would be the theoretical maximum velocity such an object could reach, if we eventually want to also decelerate to zero at some distant location? Would the speed reached be sufficient to exit the Solar system and start an interstellar voyage?

Size and mass of this space vehicle's engine is negligible, and we don't care that the projectiles might hit some other object in their way.