Q$1)$ A vertical curve will be located on a $1$st class $\backslash (3\backslash$times $3\backslash )$ highway section. The entering and exiting grades are $\backslash (+5\mathrm{.}10\backslash \%\backslash )$ and $\backslash (-6\mathrm{.}40\backslash \%\backslash ),$ respectively. The point of intersection of the tangents is at station $\backslash (2+440\backslash ),$ and its elevation is $620$ m $.$ Perception$-$reaction time is assumed to be $1\mathrm{.}5$ seconds, the friction factor is $0\mathrm{.}35,$ and the design speed is $\backslash (100\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash )$ for the road section.

a$)$ Identify and specify the type of vertical curve. Provide a clear figure showing the PVI, PVC$,$ PVT$,$ and the midpoint of the vertical curve.

b$)$ Calculate the length of the vertical curve.

c$)$ Assess whether the calculated vertical curve length meets the minimum conditions.

d$)$ Find the elevation and stationing of the points of vertical curvature $($PVC and PVT$)$ and the midpoint of the vertical curve.

e$)$ Derive the equation of the vertical curve and calculate followings:

$-$ The elevation of points located at a distance of $183,277,$ and $414\mathrm{.}50$ meters from the PVC point.

$-$ The distance from points with elevations of $\backslash (610\mathrm{.}82,612\mathrm{.}20\backslash ),$ and $603\mathrm{.}70$ to the PVC point.

f$)$ Provide grade elevations at every $60$ meters along the curve. Tabulate the calculations and results. $($You are expected to present the results on a table.$)$