problem $1(20$ points$)$: Green$-$Ampt Infiltration Model. A rainstorm of constant intensityproduces $1\mathrm{.}6$cm of rainfall in $2$ hours on a loam soil $($porosity n$=0\mathrm{.}55,$ hydraulic conductivity K$=\mathrm{.}1$cm$/$hr$,$ and wetting front soil suction head $=20$cm$).$ The soil moisture content prior to the storm is $15\%.$

a$)$ Compute the cummulative infiltration F and the infiltration rate f at t $=1$ hour.

b$)$ Calculate the cummulative infiltration F$,$ infiltration rate f$,$ and cummulative excess rainfall $($or surface runoff$)$ at the end of the storm $($i$.$e$.,$ at t $=2$ hours$)?$