Q$1(35$pts$).$ A $224,8$ m equal$-$tangent sag vertical curve has the PVC at station $2+282\mathrm{.}500$ and elevation $105\mathrm{.}400$ m The initial grade is $-3\%,$ and the final grade is $+1\%.$

Determine a$)$ the stationing,

b$)$ elevation of the PVI, the PVT

c$)$ the lowest point on the curve.

St$.$ Km PVC: $2+282\mathrm{.}500$

Elevation PVC: $105\mathrm{.}400$ m