Section III: $(15$ points$)$

A vehicle is approaching a two$-$lane highway at a speed of $100mph.$ A horizontal curve is

designed for that highway. It is a $3-$degree curve $(D)$ of length $1,500ft.$ The lane width is $12$

ft$.[15$ points$]$

$($a$)$ What is the radius of curvature $(R)$ and central angle of the curve $()$

$($b$)$ Can this vehicle navigate the curve safely without sliding? And why?