Given the following vertical alignment. Grade $1=2\%$ downgrade to a point of vertical intersection $($PVI$)$ at station $110+00$ at elevation $500$ feet. From the PVI Grade $2$ is $1\mathrm{.}5\%$ upgrade. Determine the following for and $45-$mph design speed:

a$)$ The vertical curve $K$ value that satisfies minimum stopping sight distance $(1$ mark$)$

b$)$ Using the above K value determine the length of vertical curve $(1$ mark$)$

c$)$ Determine the elevation of the PVC $(1$ mark$)$

d$)$ Determine the station of the lowest point $($one mark$)$