shooting yourself down - more physics?

In article ,
"Rich S." wrote:

Smitty Two asked:

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?

Before you find yourself in the same trap as me, let me ask for some
clarification:

1. Since you stipulate a vacuum, are we flying above the Earth?
2. How high?
3. Are we flying at an absolute altitude, e.g. following an orbital path?
4. Is the plane flying level at the moment of firing with only the gun
pointed up at the target airplane?

Rich "Without a clue" S.

I think I'm already in that trap, but it wasn't my intention (or yours,
I know) for this to be a trick question based on ambiguity in the
phrasing.

But, sure, I'll address your concerns.

1. I didn't stipulate a vacuum. My engine and wing don't work very well
without air. I said, to simplify calculations, ignore the effects of
friction on the projectile. We are flying above the earth.

2. At an altitude at which acceleration due to gravity is 32 feet per
second per second. Assume this remains constant throughout.

3. With the exception of the airplanes and the guns, this is a
pre-Columbian question. The earth is flat. Or, if you prefer, we're
flying tangentially to its curved surface.

4. The plane is flying level, as I believe I stated.