Speed Conversion

First, convert the given speed from kilometers per hour (km/h) to meters per second (m/s) for consistency with distance units.

$ \text{Speed} = 36 \text{ km/h} = 36 \times \frac{1000 \text{ m}}{3600 \text{ s}} = 10 \text{ m/s} $

Traffic Headway Calculation

The time headway is the time interval required for a vehicle and its mandated safety gap to pass a specific point. This value is crucial for determining traffic flow rates.

Car Headway

Calculate the time headway for cars:

• Car Length = $5 \text{ m}$
• Required Gap after Car = $15 \text{ m}$
• Effective Distance per Car = Car Length + Required Gap = $5 \text{ m} + 15 \text{ m} = 20 \text{ m}$
• Time Headway for Car ($T_C$) = $ \frac{\text{Effective Distance}}{\text{Speed}} = \frac{20 \text{ m}}{10 \text{ m/s}} = 2 \text{ s} $

Truck Headway

Calculate the time headway for trucks:

• Truck Length = $10 \text{ m}$
• Required Gap after Truck = $20 \text{ m}$
• Effective Distance per Truck = Truck Length + Required Gap = $10 \text{ m} + 20 \text{ m} = 30 \text{ m}$
• Time Headway for Truck ($T_T$) = $ \frac{\text{Effective Distance}}{\text{Speed}} = \frac{30 \text{ m}}{10 \text{ m/s}} = 3 \text{ s} $

Alternating Vehicle Flow

Since cars and trucks use the bridge alternately (e.g., Car, Truck, Car, Truck,...), the time headway experienced by traffic flow alternates between $T_C = 2 \text{ s}$ and $T_T = 3 \text{ s}$.

Average Headway for Maximum Flow

To find the maximum number of vehicles per hour, we compute the average time headway over a cycle comprising one car and one truck.

$ T_{avg} = \frac{T_C + T_T}{2} = \frac{2 \text{ s} + 3 \text{ s}}{2} = \frac{5 \text{ s}}{2} = 2.5 \text{ s} $

Maximum Vehicles Per Hour Calculation

An hour consists of $3600$ seconds. The maximum number of vehicles is determined by dividing the total time by the average headway.

Maximum Vehicles = $ \frac{\text{Total Seconds in an Hour}}{\text{Average Headway}} = \frac{3600 \text{ s}}{2.5 \text{ s/vehicle}} = 1440 \text{ vehicles} $