Problem $4$: Vertical Curve $-$ overhead obstructions

A vertical curve is used to connect a $2\%$ downgrade starting at an elevation of $150$ feet

followed by a $1\mathrm{.}5\%$ upgrade. The length of the curve is $1,000$ feet. An overhead guide sign is

being placed over the PVI of this curve.

a$.$ Identify the vertical curve type.

b$.$ Compute the function for the curve elevation.

c$.$ Assume an $8ft$ tall truck, with a driver eye height at $5ft$ must be able to see the

object at least $2ft$ tall throughout the curve. The truck has a deceleration rate at

$a=10f\frac{t}{s^2},$ a perception$-$reaction time of $2\mathrm{.}5s,$ and a speed of $70mph.$ Assume a

minimum sign height of $11ft$ above the roadway surface to allow for vehicles to

pass under the sign.

i$.$ Calculate the stopping sight distance for these conditions.

ii$.$ At what height above the roadway should the bottom of the sign be

placed?