Assumptions:

- numbers given are pounds-mass
- nozzle is 4 feet long

The fuel accelerates from zero to 6600 ft/sec in a distance of 4 feet. Therefore the fuel is accelerated at a rate of approximately 5,445,000 ft/sec^2 over a timespan of 1.2 milliseconds.

Four thousand pounds of fuel is burned in one minute, or 0.08 pounds per 1.2 milliseconds.

F = ma = 435,600 pounds thrust

Plugging that into my own personal rocket equation I get a velocity at burnout of 2468 ft/sec (Mach 2.236) at an altitude of 51,074 ft. The rocket would theoretically coast to an apogee of 146,246 ft (27.7 miles), all neglecting aerodynamic drag of course.

If you add the extra 513 ft/sec from the cannon launcher you get an apogee of 189,923 ft (36 miles). If the rocket fail to fire it'll coast to only 4086 feet apogee. All of this neglects air resistance of course.

What about air resistance? The rocket diameter is 4.33 ft, and I assume is composed of a long cylinder with a cone on top. If the cone is 10 feet high then its solid angle is 24.45 deg. From a neat little chart I have I can look up the drag coefficient, which turns out to be about 0.5. Neat eh? I can turn out numbers just like that... Just like that! :-)

Air resistance varies with velocity, but we can assume it varies linearly (even though it doesn't). But anyways, at maximum velocity the drag would be about 52,195 pounds-force. Since we are assuming this varies linearly, then the average drag on this rocket before burnout is approx. 26,100 lbs-force. We can subtract this from the thrust, which was 435,600 pounds-force, but now works down to about 409,500 pounds force.

With this new value for thrust, I can rework my rocket equation (gawd this is starting to suck, damn imperial units!) to get a new velocity at burnout of 2363 ft/sec. This would make negligible difference in the altitude at apogee IMO.

So, this sucker should go 36 miles high. If he forgoes the cannon launcher, he'll still get up to 27.7 miles altitude. He better be wearing an oxygen mask, and a pressure suit. And with the g-forces he's expecting I would include some serious automation, cause he'll black out for sure.