With those calculations the 50,000 BTU burner should raise it 100F in less than 9 minutes. That is not going to happen.
This is because the rate at which your water temp will rise is dependent on how much total energy is added to the water, not just how much comes out of the burner. This means you need to account for the efficiency of heat transfer from your burner to the water- this will be a fairly low efficiency in a standard burner setup.
This will be dependent on lots of factors like the shape and material of your kettle, the atmospheric temperature and humidity may come into effect (to what degree I am not sure though it should affect the thermal conductivity of the air). There are probably other factors I am leaving out.
Now if you could get 100% heat transfer with no other losses... those calculations would be right on the money.
So no you will not heat water in 2 minutes with a 200,000 btu burner even if it did put out the rated heat.
This burner is the one I have and is rated at 200,000 BTU
http://www.amazon.com/Bayou-Classic-KAB4-Pressure-Cooker/dp/B0009JXYQY/ref=sr_1_1?ie=UTF8&qid=1339089754&sr=8-1
The part about it I like a lot is that larger volumes are handled well and it is far quieter than the jet burners. You can run it fairly low and get a good boil without the loud sound. You don't really use all 200,000 BTUs
And no, it does not melt my kettle.. though I have a thick bottomed kettle.
Of course.. it is also likely that the BTU ratings are measured at full pressure, maximum output. This is not how you will be running it and will not get the 200,000 btu max.
I know I am not burning through propane at a rate that would give 220,000btus... propane gives about 15,000btu per pound... I would burn through nearly 15lbs in an hour at that rate. Since I can run for about 4 hours at the rate I burn with about 15 lbs of propane I figure I am putting out about an average 55,000 btu at the level I burn. Some of the time probably a good bit less and some of the time a good bit more.
So the end game is that a 50,000 BTU burner is technically plenty.