Problem $2$

A $4$ curve has $2$ tangents that intersect at $40{30}^{\text{'}}.$ Determine:

a$)$ Radius of the curve $[2]$

b$)$ Tangent length $[2]$

c$)$ If the speed limit is $55$ mph and the road is superelevated at $6\%,$ does the radius in $($b$)$ meet the minimum requirement? $[3]$

d$)$ If station PC is $500+50,$ determine the deflection angle and chord length to the next station from PC$.[3]$