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Any ballistics experts? I need some help!

I'm trying to figure out the formula (or end result thereof, if anyone is so inclined) for calculating the exact recoil value in foot-pounds of a 7-kilogram weapon firing a single 1-gram (15.4 grain) slug at a speed of 15 kilometers per second. I would have done it myself, but the problems behind that are (1) the fact that I can't find the numbers for any conventional propellant that will accelerate a slug to that speed, (2) that I'm not privy to the numbers involving current-generation Navy railgun experiments, and (3) all the formulas I've enountered thus far assume that a chemical propellant is being used to accelerate the slug. As a benchrest, I'm comparing its recoil value to a 2.7-kilogram M4A1 rifle, firing a 5-gram (77 grain) 5.56x45mm round at 2.8 kilometers per second (6 foot pounds of recoil at 8 feet per second for the M4A1 firing the round I specified). Thanks in advance to anyone who can help.

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