2 hours ?
There is no way they are going to let you get about with a placenta still inside you for two hours- australia, america, uk or ..Antartica!
When mine didn't come out within a few minutes, they were alll, "hmmm" and murmuring between themselves, and getting the head midvife in for a look.
They have to get it out before the uterus contracts around it, and the cervix starts to close- trapping it in there and causing infection- and that doesn't take long.
They do pull the cord- (read my other post), but they don't just give it a good tug!, they have to be very careful about it so as not to damage the uterine wall, to which it is attached. A very experienced midwife is the only one who should attempt it, if an obstetrition is not present.