Q$1.(40$pts$)$: A section of highway includes both horizontal and vertical curves in which their intersection points $($P$1$ hor and PVI$)$ are coinciding each other. $($Hint: They are same points$).$ Passings are not allowed throughout the curves; Two lane road, Lane Widths $=3\mathrm{.}6m.)$

The geometric data related with these curves are given below.

Vert. Curve: $g_1=+2\%$; Length: $210m.$; Elevation PVT: $480m$; Stkm PVC$=2+314$

Horizontal curve: Central Angle: $45$ ; Superelevation:$6\%$; Elevation PI hor: $484\mathrm{.}5$

a$)$ What is the type of this vertical curve? $($Decide by calculation$)$

b$)$ Find the permissible speed by using Stopping Sight Distance $($SSD$)$ vertical curve design considerations.

c$)$ Decide the radius of horizontal curve.

d$)$ Find PT of the horizontal curve.