Problem $4.$ Shear Stress$/$Viscosity $(20$ points$)$

A block of weight $W$ slides down an inclined plane while lubricated by a thin film of oil, as shown in the figure. The film contact area is A and its thickness is $h.$

a$.$ Assuming a linear velocity distribution in the film, derive an expression for the "terminal" $($zero acceleration$)$ velocity $V$ of the block.

b$.$ Find the terminal velocity of the block if the block mass is $6kg,A=35c{m}^2,=15,$ and the film is $1-$mm$-$thick SAE $30$ oil with $=0\mathrm{.}29k\frac{g}{m-s}.$

Figure for Problem $4$