ORIGINAL: sloth
I came up with 6828.16 meters. For total height. Now I haven't used my physics in 6 years but I used to be pretty proficient at it.
Calc time for height we know that the starting velocity 800m/s and the final velocity is 0 m/s(just before it starts coming down). Acceleration is a constant -9.8m/s^2. We get 0=800m/s-9.8m/s^2*t^2 which is (800m/s)/(9.8m/s^2)=t^2 which means t=9.035s.
Now distance is D=InitialVelocity*t+.5*acceleration*time^2. D=(800m/s)*(9.035s)+.5(-9.8m/ss)*(81.6ss) D=6828.16
Calculating drag depends on air density. Since that changes with altitude that is just way to much to go into.
Sloth, you are right about the difficulties of including drag. For one thing, you would have to know air density (temperature and altitude, AKA density altitude) at the time the shot is fired, and also the ballistic coefficient of the particular projectile used. However, it seems to me that drag is THE major factor that causes a bullet to lose forward momentum unless it hits something more substantial than air. Therefore, to ignore it is to overlook the major limiting factor on the vertical distance any gun can shoot. Early ballisicians had a devil of a time trying to produce firing tables for cannon because they were not certain the extent to which air resistance affected their projectiles, until they invented the ballistic pendulum and were able to determine cannon ball velocities near the muzzle and at extended distances. They were just amazed to discover just how much velocity was lost due to drag.