What is the trajectory of a 223 sighted in at 50 yards?

The trajectory is always straight out the front of the barrel. If you are referring to the velocity of the projectile at 50 yards, that would depend on the charge in the round, the length of the barrel, and the grain weight of the projectile. In any event, a good book like Lyman's Handloading would give you that sort of data. The range, however, is generally between 2500 - 3200 feet per second.