Problem $1[10$pts$]$

A vertical curve is to be designed to join an incoming $\backslash (+2\mathrm{.}3\backslash \%\backslash )$ grade with an outgoing $\backslash (2\mathrm{.}1\backslash \%\backslash )$ grade at a section of a two$-$lane highway.

a$)\backslash ([3\backslash$mathrm$\{$pts$\}]\backslash )$ Determine whether this is a crest or a sag curve.

b$)[7$ pts$]$ Determine the minimum length of the curve if the design speed of the highway is $60$ miles per hour and if the stopping sight distance $\backslash ($ S $\backslash )$ is less than the design length of the curve $\backslash ((\backslash$mathrm$\{$S$\}<mi>\backslash </mi>$mathrm$\{$L$\})\backslash ).$ Here, we assume that the coefficient of friction on road is $0\mathrm{.}35$ and that the perception and reaction time is $2\mathrm{.}5$ seconds.