$(15$ Points$)$ A highway reconstruction project is being undertaken to reduce crash rates. The

reconstruction involves a major realignment of the highway such that a $60-m\frac{i}{h}$ design speed is

attained. At one point on the highway, an $800-ft$ equal$-$tangent crest vertical curve exists.

Measurements show that at $3+52$ stations from the $PVC,$ the vertical curve offset is $3ft.$ Assess

the adequacy of this existing curve in light of the reconstruction design speed of $60m\frac{i}{h}$ and, if

the existing curve is inadequate, compute a satisfactory curve length.