A soil survey revealed a map unit that has soil porosity ${}_s=0\mathrm{.}453c\frac{m^3}{c}{m}^3,$ initial soil water content ${}_i=0\mathrm{.}041c\frac{m^3}{c}{m}^3,$ wetting front capillary pressure head ${}_f=-11cm,$ and saturated hydraulic conductivity of $K_s=1\mathrm{.}09c\frac{m}{h}r.$ A rainfall event of uniform rain intensity $=7c\frac{m}{h}r$ and duration of $48$ hours took place over this map unit area.

Find using the Green$-$Ampt model, a$)$ the infiltration rate $)$ versus the cumulative infiltration $($ cm $)$ curve after the time of ponding $($of soil surface saturation$)$ until $t=8hr$ over this map unit area under the above$-$described rainfall event when $6\mathrm{.}2$ cm depth of ponded water formed over the soil surface at the time of ponding; and

b$)$ the cumulative infiltration $(cm)$ versus time $($hr$)$ after the time of ponding until $t=8hr$ for the above$-$described rainfall event when $6\mathrm{.}2$ cm depth of ponded water formed over the soil surface at the time of ponding.

GRAPH AND TABULATE YOUR RESULTS. ALL COMPUTATIONS MUST BE SHOWN IN DETAIL.