$4.(20$ Pts$)$ An unlined trapezoidal earth channel with a bed slope of $0\mathrm{.}0009$ needs to be designed to carry a flow of $75$ cfs $.$ A side slope of $2$ horizontal to $1$ vertical is required. The Manning's n is estimated at $0\mathrm{.}022.$ Determine the bottom width and flow depth if the maximum permissible velocity to prevent erosion is $2\mathrm{.}80$ fps $.$