Problem $1.$ A horizontal curve is being designed through mountainous terrain for a four$-$lane road with lanes that are $10ft$ wide. The central angle is known to be $40$ degrees, the tangent distance is $510ft,$ and the stationing of the tangent intersection $($PI$)$ is $2700+00.$ Under specified conditions and vehicle speed, the roadway surface is determined to have a coefficient of side friction of $0\mathrm{.}12,$ and the curve's superelevation is $0\mathrm{.}054f\frac{t}{f}t.$ What is the stationing of the $PC$ and PT$?$ What is the design speed?

Problem $2.$ A developer is having a single$-$lane raceway constructed with a $100mph$ design speed. A curve on the raceway has a radius of $1,000ft,$ a central angle of $30$ degrees, and PI stationing at $1,125+00.$ If the design coefficient of side friction is $0\mathrm{.}20,$ determine the superelevation required at the design speed $($do not ignore the normal component of the centripetal force$).$ Also, compute the degree of curve, length of curve, and stationing of the PC and PT$.$

Problem $3.$ Textbook $($Mannering & Washburn, $5^{th}$ edition$)$ #$3\mathrm{.}36$

Problem $4.$ Design a horizontal curve on a level, two$-$lane highway $($lane width is $12ft).$ Central angle is $14$ degrees. Radius is $2,100$ ft$.$ Design speed is $80mph.$ What distance must be cleared from the inside edge of the inside lane? In class, we found the practical value using the shorthand equation for Ms$,$ Is that value accurate? Find the accurate value and explain why in practice engineers always use short$-$hand equation even when SSD is longer than L$.$

Problem $5.$ You are asked to design a horizontal curve for a two$-$lane road. The road has $12-ft$ lanes. Due to expensive excavation, it is determined that a maximum of $34ft$ can be cleared from the road's centerline toward the inside lane to provide for stopping sight distance. Also, local guidelines dictate a maximum superelevation of $0\mathrm{.}08f\frac{t}{f}t.$ What is the highest possible design speed for this curve?