Problem $4$: For the given failure surface, determine the factor of safety in terms of total stress for the slope detailed below. The unit weight for both soils is $19k\frac{N}{m^3}.$ For soil $1,$ the relevant shear strength parameters are $c_u=20k\frac{N}{m^2}$ and ${}_u=0,$ and for soil $2,c_u=35k\frac{N}{m^2}$ and ${}_u=0.$

$(10$ points$)$