Problem $3.(25$pts$)$A single film of liquid flows down an incline as shown in the picture below. The bottom wall also moves upwards with a velocity of $U.$ Answer the questions below. You may assume that the liquid has constant fluid properties and is Newtonian.

a$)$ Write out the entire x $-$momentum equation for the appropriate velocity component, including all terms. Simplify this equation justifying each simplification step. You must provide justification for your simplifications.

b$)$ List the boundary conditions that are appropriate to this problem.

c$)$ Solve for the resulting velocity profile in the liquid layer.