shooting yourself down - more physics?

If you guys aren't tired of arithmetic, I'm wondering if any fighter
pilots have shot themselves down. Probably not, but imagine you're
flying straight and level at 1000 mph and fire a 500 mph projectile at
an enemy that's directly ahead but at a higher altitude. You miss him;
the bullet follows a parabolic path, returning to your altitude just as
you overtake it. Discounting air friction, at what angle was the bullet
fired?

(extra credit question -- how many rivets could you have installed in
the time you wasted thinking about this question?)