$(20$pts$)$ A two$-$lane highway $($two $12-$ft lanes with negligible shoulders$)$ has a posted speed limit of $50$ mph $,$ and on one section, has both horizontal and vertical curves as shown in the figure below.

A recent daytime accident $($driver traveling eastbound struck a stationary roadway object$)$ resulted in a fatality and a lawsuit alleging the $50-$mph speed limit was unsafe speed for the curves in question and a major cause of the accident. Evaluate quantitatively the following:

a$.$ The adequacy of horizontal sight distance,

b$.$ The adequacy of the roadway horizontal curvature, and

c$.$ The adequacy of the vertical curvature.

d$.$ Do you agree that the $50-$mph speed limit was unsafe speed limit$,$ and why?