Final answer:
Designing banked curves for mountainous terrain road requires calculating ideal speed and minimum friction for safety, considering both the slope of the bank and the effects of centrifugal force.
Step-by-step explanation:
Designing a horizontal curve for a two-lane road in mountainous terrain involves understanding the physics of banked curves. Banked curves are slopes in the road that assist vehicles in negotiating turns. An ideally banked curve is one where the angle of the slope allows a vehicle to take the curve at a certain speed without relying on friction between the tires and the road. Calculating the ideal speed for a 100 m radius curve banked at 15.0° and determining the minimum coefficient of friction needed are necessary for ensuring that cars can safely negotiate the curve. Additionally, considerations for centrifugal force must be taken into account, as this fictitious force can act to throw a vehicle off the road when it is rotating within a non-inertial frame of reference.