Imagine trying to hit something 125 miles away with a non-guided projectile (solid mass)? Non-line-of-sight, projectile weight deviations, multiple wind velocities and directions, rain pockets, natural barriers, etc... crazy.
WWII battleships did it with great accuracy at 20 miles or better.
Yeah - this is a whole lot farther, but ballistic trajectories (parabolic) are still described by the same equations - just using bigger numbers, and I’m sure adjusting for the special considerations for the super-fast launch.
Bottom line? Hitting the target will not be a problem. Artillery men have been doing it for ages.