Problem $1$: Sag Vertical Curve $($Transportation Engineering, junior course$)$

An equal tangent sag vertical curve has the following properties:

$$ The length of the vertical curve is $900$ ft

$$ PVI: Station is $475+00$ and elevation is $1235\mathrm{.}62$ ft

$$ Initial grade is $-5\mathrm{.}5\%($before PVI$)$

$$ Final grade is $+2\mathrm{.}0\%($after PVI$)$

Determine the following:

a$)$ Station and elevation of the PVC $($point of vertical curvature$)$

b$)$ Station and elevation of the PVT $($point of vertical tangency$)$

c$)$ Station and elevation at the low point on the vertical curve