$(8$ points, estimated time $10$ minutes$)$ A thin film of fluid flows past a fixed surface, as shown in the figure. Due to the no$-$slip condition, the velocity at the fixed surface is zero, and the velocity profile near the solid surface is shown in the figure. Determine the mean velocity if the velocity measured at an elevation $=4cm$ above the surface is equal to $U=4c\frac{m}{s}.$ Express your answer in $c\frac{m}{s}.$

$\frac{u}{U}=\frac{3}{2}\frac{y}{}-\frac{1}{2}(\frac{y^{-}}{}{)}^{I_3}$