III. $(20\backslash \%)$ A layer of oil is in a steady motion along a moving belt, as shown in the figure below. The belt slides upward, at an inclination $\backslash (\backslash$theta $\backslash )$ and speed $\backslash (\backslash$boldsymbol$\{$V$\}\backslash ).$ Outside the layer of oil is air at atmospheric pressure. a$)$ Let $\backslash ($ y$=0\backslash )$ be the surface of the belt and set $\backslash ($ y$=$h $\backslash )$ at the air$-$oil interface. Determine the velocity profile in the oil, $\backslash ($ u$($y$)\backslash ).$

b$)$ Determine the shear stress along the belt.

c$)$ Plot the velocity profile in the fluid using the computer $($choose reasonable values for quantities that may be needed; use either air or water$)$