A $200\text{-meter}$ equal-tangent crest vertical curve connects an ascending grade of $+3.0\%$ ($g_1$) and a descending grade of $-2.0\%$ ($g_2$). The Point of Vertical Intersection (PVI) is located at station $10+500$ with an elevation of $150.00 \text{ m}$. Determine the elevation of the curve at station $10+460$.

Using the same curve parameters as the previous example ($L = 200 \text{ m}$, $g_1 = +0.03$, $g_2 = -0.02$, $\text{PVC Station} = 10+400$, $\text{Elev}_{\text{PVC}} = 147.00 \text{ m}$), determine the station and elevation of the highest point on the curve.

A crest vertical curve must be designed to connect a $+4.0\%$ grade and a $-3.0\%$ grade. The required Stopping Sight Distance (SSD) for the design speed is $160 \text{ m}$. Assuming the driver's eye height is $1.08 \text{ m}$ and the object height is $0.60 \text{ m}$, what is the minimum required length of the vertical curve ($L_{min}$) if we assume the curve length is greater than the sight distance ($S < L$)?

A sag vertical curve connects a $-4.0\%$ grade to a $+2.0\%$ grade. The design speed requires a Stopping Sight Distance ($S$) of $130 \text{ m}$. Standard headlight height ($H$) is $0.60 \text{ m}$, and the upward divergence angle ($\beta$) of the headlight beam is $1^{\circ}$. Calculate the minimum required length of the sag curve assuming $S < L$.

A new highway alignment must cross an existing railroad track via an overpass bridge, and immediately afterward pass under a high-voltage power line corridor. Describe the sequence of vertical curves required and the primary engineering concerns for each.