$1(3$ pt$).$ The following data were obtained experimentally for a air flowing over a rough plate.

Air with a kinematic viscosity $={1\mathrm{.}4610}^{-5}\frac{m^2}{s},$ density $=1\mathrm{.}23k\frac{g}{m^3}$ where $U$ is air velocity over

the plate.

$U(y)=200[1\mathrm{.}0-e^{(-8y)}]$

$($a$)$ determine the magnitude and direction of the shearing stress at the rough surface of the plate

$($b$)$ find shear stress at free stream $(y=4m)$