A firefighter directs a horizontal stream of water toward a fire at an angle of 40° measured from the horizontal. The fire hydrant and hose deliver 93 gallons per minute
(1 gal/min = 6.31 cross product 10−5 m3/s),
and the nozzle projects the water with a speed of 6.7 m/s. How much horizontal force must the firefighter exert on the hose to keep it stationary?

Question

A firefighter directs a horizontal stream of water toward a fire at an angle of 40° measured from the horizontal. The fire hydrant and hose deliver 93 gallons per minute
(1 gal/min = 6.31 cross product 10−5 m3/s),
and the nozzle projects the water with a speed of 6.7 m/s. How much horizontal force must the firefighter exert on the hose to keep it stationary?

irishboy123 · Answer

F = dp/dt [Newton's original formulation] = d(mv)/dt = v•dm/dt + m•dv/dt

dV/dt is just a proxy for dm/dt.  introduce  a placeholder for density.  you will need to call it  µ or the equations just won't work.  µ dV/dt  = dm/dt. thus, dV/dt  = (1/µ ) * dm/dt. 

these need to be resolved in the x and y directions.