$11$ A vertical curve needs to be designed on a freeway, connecting a $4\%$ downgrade to a $2\%$ upgrade. The design speed

is $65m\frac{i}{h}r,$ reaction time is $2\mathrm{.}5$ seconds, and the coefficient of braking friction is $0\mathrm{.}348.$ Design the curve, with the

point of vertical curvature PVC occurring at station $137+03$ and elevation $7330$ feet $($that is$,$ at PVC$,$ at each whole

station, and at the point of vertical tangency, provide the curve elevation$).$