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A trajectory is the "flight path" of an object in motion, such as a shell, rocket, missile or bullet.

Trajectories become interesting to Gunners when they are interfered with by other things such as hill tops.

Trajectories become interesting to all other arms when they are on the hill top and didn't tell the Gunners they were there.

If you are seriously interested, this wiki page contains formulae and more descriptions. Or you could go out, drink beer and shag girls, which is an equally valid choice instead of this turgid subject.