why is it difficult for a fire fighter to hold a hose that ejects large amounts of water at high speed?

Answer 1

The hose experiences a backward reaction force equal to the rate that water momentum leaves the nozzle. The walls of the hose must exert this force on the water to direct it out the nozzle, and the hose feels the reaction force. If the water came straight from the hydrant to the nozzle, then there would not have to be a large force, but this is almost never the case.