$($b$)$ Using the Rankine method, design an active retaining wall against the factors of safety with respect to sliding, overturning, and soil bearing capacity of a $10-$feet$-$high vertical retaining wall. Use the Data in Table $1$ and refer to Figure $1.$ Assume that the soil has a total unit weight of $125pcf$ and a friction value of $38$ degrees. Assume that there is a uniform surcharge of $100psf$ located along the surface behind the wall and, the backfill soil does not slope. The ultimate bearing capacity of soil is $5000$ psf$.$ The Rankine active pressure coefficient $(Ka)$ is $0\mathrm{.}307$ and the design is for a unit length. Assume that reinforcement of the wall has already been designed.