A fireman standing on a 6.5 m high ladder operates a water hose with a round nozzle of
diameter 3.08 inch. The lower end of the hose
(6.5 m below the nozzle) is connected to the
pump outlet of diameter 4.51 inch. The gauge
pressure of the water at the pump is
P
(gauge)
pump = P
(abs)
pump − Patm
= 41.2 PSI = 284.064 kPa .
Calculate the speed of the water jet emerging from the nozzle. Assume that water is an
incompressible liquid of density 1000 kg/m3
and negligible viscosity. The acceleration of
gravity is 9.8 m/s
2
.
Answer in units of m/s.

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.