What is the universe expanding into?
Well, the water is basically providing thrust, like those toy rockets you used to be able to buy and hook up to your garden hose. They used water pressure to thrust the rocket up sometimes 50 feet. The fire hose is reacting to the action of the water shooting through it and, (tying it in with the first law) the firemen must act upon it with a greater force to overcome it. Basically, they wrestle it to the ground.
there is not any action and reaction involved. none what so ever. the whole phenomenon is explained by the law of conservation of momentum. it is exactly why aeroplanes accelerate, helicopters fly etc. in the system WATER-HOSE, when all the molecules of the water are thrusted in one direction, in order to conserve the momentum the hose must move at the opposite direction. unfotrunately the firemen cannot holp it completely parallele and the nozzles in front of the hose (to control and increase sprink effect) guide the water in different directions. the effect and result to it is the hos to move constantly in the opposite sirection of the water
There are several good answers here already. However, there is one other way to think of things involving 'exhaust'. There is pressure in the hose that is being balanced in every direction but one. The water that is in the hose is pushing in all directions at the same time. That is one of the qualities of a liquid under pressure. Now, there are sides to the hose that push back against the water. They seem to be in balance. There is water pressure being applied at the back of the hose from what ever the water supply is (usually 20 psi or so). But, at the front of the hose there is a big hole. Nothing is pushing against the water to keep it in the hose. This means that there is water in the hose pushing in all directions on the hose except out the front. This creates the unbalanced force. For a 1 inch nozzle on the hose with 20 psi, you would get over 60 pounds of back pressure from the hose.
An idea I've toyed with for years; get an old four cylinder engine and mount it on a frame outside the house. Attach a generator to it, one big enough to run the whole house. The engine is a bit OVERKILL but you can plumb the radiator into the house and use the heat from the engine to warm the house while the electrical generator supplies all the electrical needs. If you have forced hot air heat you can (if you're crafty) install a radiator inside the return air duct and run the fan on constant so you keep the engine from overheating while you heat the house. If the house gets too warm you can open a window or two and let cool, fresh air in. To this date I've not pursued that idea any further than JUST an idea. But I have made drawings and done calculations on it. Even figured out how to run the engine on natural gas. Therefore I'd have a constant source of electricity and heat during winter, should the need arise. If there were to be a power failure, a simple diverter valve can send the hot water from the engine outside without having to add heat to the house. Radiator inside, radiator outside. Depending on the need, switch back and forth. Electrical power supplied by a gas engine and generator running off of the natural gas supply coming into the house. Hope this helps. '')
action and reaction is the answer to your question..it usually takes two firemen to hold the hose and keep it directed on the firethere is a lot of pressure at the exit point..