$(20$ points$)$ A solid cube with a side length of $1\mathrm{.}0ft$ and a weight of $400lb$ slides

down a smooth surface that is inclined at $45$ degrees to the horizontal. The block

slides on a film of oil with a viscosity of $1\mathrm{.}85{10}^{-2}lb-\frac{s}{f}{t}^2.$ If the velocity of the

block is $1\mathrm{.}0f\frac{t}{s},$ determine the thickness of the oil film assuming a linear velocity

distribution in the film. Give your answer in feet.