An engineer is checking the design of a crest vertical curve to ensure it meets the sight distnce requeriement. If the design value of K of the curve is $151,$ answer the folowing:

$(1)$ Determine the maximum design speed in mph for this curve, and

$(2)$ Compute the stopping sight distnace $($SSD$)$ in feet that corresponds to the design speed determined in part $(1)$ above assuming S$$L$.$ How does this SSD value compare to that obtained with the AASHTO method?

$(3)$ Determine the station of the highest point on the curve if the station of the point of BVC is $16+55\mathrm{.}0$ in the initial grade $($g$1)$ is $0\mathrm{.}6\%.$