$15$ pts $1.$ For rectangular channel, if the post$-$jump water depth, $y_2,$ is given, the pre$-$jump water depth, $y_1,$ can be

computed using the formula of $\frac{y_1}{y_2}=\frac{1}{2}(\sqrt[\phantom{2}]{1+(F_{r,2}{)}^2}-1),$ where $Fr,2$ is the Froude number at the

post$-$jump section. Show your works to derive this formula.