An intersection approach has a design speed of $60 \text{ km/h}$ on a level grade ($0\%$). The intersection width ($W$) is $18 \text{ meters}$, and the average vehicle length ($L$) is $6 \text{ meters}$. Assuming a standard driver perception-reaction time ($t$) of $1.0 \text{ second}$ and a comfortable deceleration rate ($a$) of $3.0 \text{ m/s}^2$, calculate the required yellow change interval ($Y$) to eliminate the dilemma zone.

A four-way intersection between a Major Street (2 lanes total) and a Minor Street (1 lane each approach) is being evaluated for a traffic signal using the MUTCD Eight-Hour Vehicular Volume warrant (Warrant 1). To meet the warrant under Condition A (Minimum Vehicular Volume), the major street must have at least $500 \text{ veh/hr}$ (total both approaches) and the minor street must have at least $150 \text{ veh/hr}$ (highest volume single approach) for each of any $8 \text{ hours}$ of an average day.

Traffic counts show that for $9 \text{ hours}$ of the day, the Major Street volume fluctuates between $600$ and $850 \text{ veh/hr}$. During those same $9 \text{ hours}$, the highest minor street approach volume fluctuates between $120$ and $140 \text{ veh/hr}$. Does this intersection meet Warrant 1, Condition A?

A standard broken yellow centerline on a rural highway requires a $3 \text{ meter}$ painted stripe followed by a $9 \text{ meter}$ unpainted gap. If a contractor is hired to paint a $12 \text{ kilometer}$ stretch of this highway, calculate the total length of paint actually required and the total number of painted stripes.

A city is upgrading the traffic signals along a major arterial corridor that connects downtown to the suburbs. The corridor features two types of intersections:

1. The downtown grid, where blocks are short, traffic is heavy in all directions, and speeds are low.
2. The suburban fringe, where the arterial crosses minor residential streets. Traffic on the minor streets is sparse but occasionally experiences brief surges when a shift ends at a nearby factory.

Recommend the type of signal controller (Pre-timed, Semi-Actuated, or Fully Actuated) for both environments and justify your choice.

A sharp, unexpected horizontal curve is located on a rural highway immediately after a long, straight tangent. There is a history of vehicles running off the road at this location. A junior engineer proposes placing a large green sign reading "Curve Ahead" right at the start of the curve. Evaluate this proposal based on the principles and categories of traffic control devices.