in a single direction $($as shown below in Fig. $3,$ along $x),$ creating a shear stress ${}_{\text{s}\text{u}\text{r}\text{f}}$ on the surface of the lake. The density of water is ${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=1000k\frac{g}{m^3}$ and the viscosity is ${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=1*{10}^{-3}N-\frac{s}{m^2},$ while for air, they are ${}_{\text{a}\text{i}\text{r}}=1\mathrm{.}23k\frac{g}{m^3}$ and ${}_{\text{a}\text{i}\text{r}}=1\mathrm{.}85*{10}^{-5}N-\frac{s}{m^2}.$

Figure $3$: Velocity profiles across a lake surface in Problem $3.$

$($a$)$ Using the information provided, determine the shear stress ${}_{\text{s}\text{u}\text{r}\text{f}}$ at the surface of the water. It will be the same whether you use properties of air or properties of water in your calculation.

$($b$)$ Determine the velocity of the water surface.