Sand from a stationary hopper falls onto a moving conveyor belt at the rate of dm/dt = 5 kg/s as shown. The conveyor belt is supported by frictionless rollers and moves at a constant speed of v = 0.75m/s under the action of a constant horizontal external force ~Fext supplied by the motor that drives the belt.
a. Find the sand's rate of change of momentum in the horizontal direction.
b. Find the force of friction exerted by the belt on the sand.
c. Find the power required by ~Fext.