Aye, but that's assuming you have an initial velocity. Remember, we're accellerating a MUCH larger mass, with stronger forces at play. Longbow was supposed to launch at Mach 9. Modern railguns launch at around Mach 7, however, Erinaum has had railguns for a while, so there might be some room for improvement in that way. However, this would require a longer barrel, and rails with a larger radius, as well as a huge charge of (as I predict by looking at modern models), 90+ MJ per shot.
I am actually thinking of making the longbow assembly replacable and allow for refitting barrels by varying size, as well as the loading system, which is currently set for 7.5 inch shells, to have varying sizes. This way, we could potentially fire smaller shells greater distances.