shooting yourself down - more physics?

Smitty Two wrote:

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.

You said discounting air friction. This is key to the problem. No air
friction would be the physical equivalent of being in a vacuum.

If there were no air friction, the projectile would continue ahead with
a forward speed of 1500 mph - its own 500 mph from its spent propellant
charge, and the 1000 mph imparted to it from the airframe.

Air friction, however, acts on the projectile from the moment it departs
the muzzle, and acts to slow the projectile in a continuous manner. The
aircraft continues to maintain its 1000 mph since it has a propulsive
device that is assumed to continue to operate. Air friction (along with
gravity) are the forces that conspire to ALLOW the aircraft to overtake
its projectile and contribute to shooting itself down.

So... are we or are we not including air friction? If we are, I am not
going to hazard a guess.. my math gland atrophied long ago after I
passed calculus. If we are not, then the problem is unsolvable in level
flight on earth.

Dave