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 On your way home from work a light turns yellow ahead of you. You are too close to the intersection to stop without a heroic effort, so you proceed toward the intersection, assuming that you'll get through it before the opposing phase is unleashed. To your surprise, the intersection signal turns red before you have made it to the stop-bar. Luckily you clear the intersection, but unfortunately, the local sheriff witnessed your maneuver. As part of your plea for mercy, you mention that the signal seems to have an inadequate intergreen period that produces a dilemma zone. Your plea doesn't work and you resolve to dispute the matter in court. You return to the intersection and measure the intergreen time, using a stopwatch. It turns out to be 6 seconds. You also note the speed limit (50 mph in this case), the width of the intersection (around 60 feet), and your car's length (18 feet). The approach to the intersection is level, and you assume that the coefficient of friction is around 0.5. Because you were only paying casual attention to the road when the incident occurred, you decide to use 1 second as your perception reaction time. Can you successfully argue that a dilemma zone exists? If one exists, what should be done to the intergreen time to fix the problem? [Solution Shown Below]
Solution The first step in this analysis is to calculate the minimum stopping distance you had under the given circumstances. The minimum safe stopping distance can be calculated using the formula below. SD = 1.47*Vo*tr + (1.47*Vo)2/(30*[f ± G]) Placing the given information into the equation yields: SD = 1.47*50*1 + (1.47*50)2/(30*[0.5±0]) Solving this equation gives us a stopping distance of 434 feet. Next you must calculate the time required to traverse the sum of the stopping distance, intersection width, and one car length. This will give you the intergreen time that is necessary for a car to safely pass through the intersection from the point-of-no-return. The intersection clearance time is given by the equation below. T = (SD + L + W)/(1.47*Vo) Placing the given information into the equation yields: T = (434 + 18 + 60)/(1.47*50) Solving this equation gives us an intersection clearance time of 7 seconds. Since the intersection clearance time provided was only 6 seconds, and a full 7 seconds is required for a car to safely pass through the intersection from the point-of-no-return, your claim that a dilemma zone exists is well founded. To fix the problem, the city should increase the intergreen time by 1 second.
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