$(25$pts$)$ Problem $2.$ A horizontal curve on a single$-$lane freeway ramp is $400$ ft long, and the design speed of the ramp is $45m\frac{i}{h}.$ If the superelevation is $10\%,$ the limiting side$-$friction coefficient is $0\mathrm{.}145,$ and the station of the $PC$ is $17+35,$ what is the station of the PI and how much distance must be cleared from the center of the lane to provide adequate stopping sight distance $($SSD$)?$ SSD design values can be looked up using Table $1.$

Table $1.$ Stopping Sight Distance $($AASHTO$,$ A policy on geometric design of highways and streets, Washington D$.$C$.2001)$

$\backslash$table$[[$us Customary$],[$Design speed $($mph$),$Brake reaction distance $($ft$),$Braking distance on level $($ft$,$Stopping sight distance$],[\backslash$table$[[$Calculated$],[($ft$)]],\backslash$table$[[$Design$],[($ft$)]]],[15,55\mathrm{.}1,21\mathrm{.}6,76\mathrm{.}7,80],[20,73\mathrm{.}5,38\mathrm{.}4,111\mathrm{.}9,115],[25,91\mathrm{.}9,60\mathrm{.}0,151\mathrm{.}9,155],[30,110\mathrm{.}3,86\mathrm{.}4,196\mathrm{.}7,200],[35,128\mathrm{.}6,117\mathrm{.}6,246\mathrm{.}2,250],[40,147\mathrm{.}0,153\mathrm{.}6,300\mathrm{.}6,305],[45,165\mathrm{.}4,194\mathrm{.}4,359\mathrm{.}8,360],[50,183\mathrm{.}8,240\mathrm{.}0,423\mathrm{.}8,425],[55,202\mathrm{.}1,290\mathrm{.}3,492\mathrm{.}4,495],[60,220\mathrm{.}5,345\mathrm{.}5,566\mathrm{.}0,570],[65,238\mathrm{.}9,405\mathrm{.}5,644\mathrm{.}4,645],[70,257\mathrm{.}3,470\mathrm{.}3,727\mathrm{.}6,730],[75,275\mathrm{.}6,539\mathrm{.}9,815\mathrm{.}5,820],[80,294\mathrm{.}0,614\mathrm{.}3,908\mathrm{.}3,910]]$

Note: Brake reaction distance is based on a time of $2\mathrm{.}5$ s ; a deceleration rate of $11\mathrm{.}2f\frac{t}{s}2$ is used to determine the calculated stopping sight distance.