Is the trajectory parabolic or elliptical?

[farolero]

Parabolic shooting is a kind of orbit interrupted by the ground.

So I was wondering if I could calculate speeds of the bullet accounting for conservation of angular momentum.

Would this diagram be correct?

 

[nasu]

Why don't you try yourself to see if the result is compatible with the one obtained by using the laws of motion for projectile in uniform field?

 

[Dale]

Parabolic shooting is a kind of orbit interrupted by the ground

Not really. A parabola comes from assuming a uniform gravitational force. When you talk about orbits you are talking instead about a central force. It would be the tip of an ellipse, not a parabola.

Edit: sorry @nasu I basically fed him the info you were trying to get him to discover.