PROBLEM $1(20$ points$)$: A block of mass $m$ is sliding down an incline with an angle $$ from the horizontal, on a thin film of oil. The gravity vector points down in the vertical direction. The thickness of the fluid film layer is $h$ and the area of the block contacting the fluid is $A.$ The viscosity of the oil is $.($a$)$ Derive an expression for the terminal velocity, $V_B,$ of the block as a function of these parameters. $($b$)$ Given that the block has a contact area of $0\mathrm{.}05m^2.$ The thickness of the fluid film is $1$ mm $,$ the fluid has a viscosity of $0\mathrm{.}38Pa-s,$ the mass of the block is $2\mathrm{.}5$ kg $,$ at what angle $$ will the block reach a terminal velocity of $1\mathrm{.}0\frac{m}{s}?$ Assume the velocity distribution in the fluid is linear.