Nearly frictionless vertical guide rails maintain a plate of mass mp in a horizontal posit...

Nearly frictionless vertical guide rails maintain a plate of mass mp in a horizontal position, such that it can slide freely in the vertical direction. A nozzle directs a water stream of area A against the plate underside, The water jet splatters in the plate plane, applying an upward force against the plate. The water flow rate  can be controlled. Assume that distances are short, so the velocity of the rising jet can be considered constant with height, (a) Determine the minimum mass flow rate  necessary to just levitate the plate and obtain a relation for the steady-state velocity of the upward moving plate for . (b) At time t= 0, the plate is at rest, and the water jet with  mmin is suddenly turned on. Apply a force balance to the plate and obtain the integral that relates velocity to time (do not solve).