Didn't they have to drop out of warp drive to fire?Couple other things springing to mind...
Space battles & lasers. We've got ships traveling at multiples of the speed of light, shooting light beams at each other? (I know, that's part of the justification in the Trek universe for the photon torpedoes, though they never really seemed to hold fast to that rule...)
The easy answer is you make up some sort of inertial dampener; evolved from the tractor beam.In Abrams's movie... Kirk & Sulu are falling over Vulcan. Chekhov sprints from the bridge to a transporter room, managing to take over & lock onto them before they hit the ground? How high up were they? How fast is Chekhov, anyway?