Question #$1(10$ points$)$: A vertical curve connects a $4\mathrm{.}4\%$ grade with a $-6\mathrm{.}8\%$ grade. The PVI is at station $(43+16)$ at an elevation of $378m.$ The design speed is $50k\frac{m}{h},$ brake reaction time $=2\mathrm{.}5s,$ and braking acceleration $=3\mathrm{.}41\frac{m}{s^2}.$ Find:

a$)$ Length of Curve $($L$).$

b$)$ Find the stations and elevations for the PVC $($or BVC$)$ and PVT $($or EVC$).$

c$)$ Find the elevation and station of the highest point on the curve.