how dumb do you have to be to open a topic with this title while you're eating
I'll be honest, I'm eating bacon baguettes at the moment and I feel fine.
not from your rectum, I don't think so. but just at some point in your intestines, probably
I don't think you could throw up something located beyond your stomach.
From your stomach to your intestines is a large number of sphincters and similar valves which prevent items going back up to the stomach and stops things from endlessly going from your stomach to your intestines.
When you throw up your body forces muscles near the stomach to force the contents back up to your throat.
I don't think it has any control over the muscles below the stomach, nor are there muscles capable of forcing the contents back up against the force of gravity.
It wouldn't be poo anyway, since brown poo is only really located in the large intestine/colon/rectum.
It's still mostly a yellowy liquid in the lower intestine, as most of the water content is still there.
If actual poo had traveled from the end of your digestive tract back up then you'd probably feel it and be in some considerable pain.
Brown vomit is likely due to the content of the vomit, as Valkerone's link explains.
Your brown vomit is likely nothing to be concerned about, other than being due to what you ate.
Just get a doctor's advice if stomach pains continue or vomiting does. If vomiting does continue try not to visit a doctor or the A&E, but phone them. You don't want to go to such a location if you're possibly infectious.
