Use the analysis of gradually varied flow step method to estimate the distance from the channel obstruction where the depth equals $8$ feet upstream to the location of the hydraulic jump where the depth is $4\mathrm{.}45$ feet. Provide the total distance to the jump as well as a profile plot with the water surface elevation $($not depth$)$ plotted along the length of the channel. Assume that the elevation of the channel bottom is $0$ feet at the location of the channel obstruction.