QQuestionCivil Engineering
QuestionCivil Engineering
10. Determine is a Dilemma Zone exists for the following situation: An intersection is 90 feet wide. The yellow time is 3.5 seconds, the speed is 40 mph, and the length of a vehicle is 20 feet. Assume a deceleration rate of 10 ft/sec/sec and a perception/reaction time of 1 second. Is there a dilemma zone? If so, how long is it?
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Answer
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Step 1:I'll solve this step by step, carefully following the LaTeX formatting guidelines:
Step 2:: Convert Speed to Feet per Second
v = 40 \frac{\mathrm{miles}}{\mathrm{hour}} \times \frac{5280 \mathrm{feet}}{1 \mathrm{mile}} \times \frac{1 \mathrm{hour}}{3600 \mathrm{seconds}} = 58.67 \frac{\mathrm{feet}}{\mathrm{seconds}}
Step 3:: Calculate Perception/Reaction Distance
d_{PR} = v \times t_{PR} = 58.67 \frac{\mathrm{feet}}{\mathrm{seconds}} \times 1 \mathrm{second} = 58.67 \mathrm{feet}
Step 4:: Calculate Braking Distance
Using the formula $$d_{brake} = \frac{v^{2}}{2 \times a}
d_{brake} = \frac{(58.67)^{2}}{2 \times 10} = 171.78 \mathrm{feet}
Step 5:: Total Stopping Distance
d_{total} = d_{PR} + d_{brake} = 58.67 + 171.78 = 230.45 \mathrm{feet}
Step 6:: Yellow Time Stopping Distance
d_{yellow} = v \times t_{yellow} = 58.67 \frac{\mathrm{feet}}{\mathrm{seconds}} \times 3.5 \mathrm{seconds} = 205.35 \mathrm{feet}
Step 7:: Dilemma Zone Calculation
\text{Dilemma Zone} = d_{total} - d_{yellow} = 230.45 - 205.35 = 25.10 \mathrm{feet}
Step 8:: Intersection Width Comparison
Intersection width = 90 feet Dilemma zone length = 25.10 feet
Final Answer
This means there is a short region where a driver cannot safely stop or proceed through the intersection during the yellow light.
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