$(20$ points$)$ The Green$-$Ampt equation for infiltration losses can be written as:

$f=K_s(1-\frac{M_d}{F}),$ where $M_d={}_s-{}_i$

The soil properties are: hydraulic conductivity is $2\mathrm{.}2i$n$/$hr; suction head is $-170\mathrm{.}2$ mm ; an effective initial saturation is $33\%$; soil porosity is $0\mathrm{.}523,$ and effective porosity is $0\mathrm{.}318.$ The rainfall intensity is always $4\mathrm{.}65i$n$/$hr$.$

a$)(10$ points$)$ Calculate the ponding time $t_p.$

b$)(5$ points$)$ Develop a plot of infiltration capacity $f$ vs infiltration volume manually draw this plot on your answer sheet, but please display the critical points.

c$)(5$ points$)$ Determine the infiltration rate $($ f $)$ when the cumulative infiltration $F=8\mathrm{.}5$ cm$.$