$3.(10$ points$)$ A trapezoidal channel of base width $20$ ft and side slope $\backslash ($ z$=1\mathrm{.}5\backslash ),$ is laid on a slope of $0\mathrm{.}001$ and carries a discharge of $1000$ cfs $.$ The channel terminates in a free overfall and it is desired to compute the upstream water surface profile. Use one step of both the direct and standard step methods to compute the water surface elevation at the point where the velocity is $\backslash (10\backslash \%\backslash )$ greater than at uniform flow. Use a Manning's $\backslash ($ n $\backslash )$ of $0\mathrm{.}025.$ You may assume ideal conditions at the outfall. Note that if many steps are taken, the desired point is approximately $1011$ feet upstream of the outfall. Compute the error between this answer and your result. Comment on the differences.