Problem $5(50$ pts$)$

The below $12$ in diameter concrete pile has been placed into a soil with skin friction of $150$ psf and a potential bearing capacity of $200$ psf at the expected depth. Using a safety factor of $2\mathrm{.}5,$ calculate the required pile depth $h$ to resist a pile load of $2$ kips.

Note: Safty Factor $=\frac{\text{T}\text{o}\text{t}\text{a}\text{l}resistance}{\text{A}\text{c}\text{t}\text{u}\text{r}\text{a}\text{l}\text{l}\text{l}\text{o}\text{a}\text{d}\text{i}\text{n}\text{g}}$