1. the physics of intersections
But Officer!…
the physics of intersections
A Rich Context Problem

2. It was obvious, a new line of defense was needed
It was obvious, a new line of defense was needed. Reginald Bounder, PhD, professor of particle physics and colleague and fellow conference goer was of no help, he was sleeping soundly in the back.
"Sir, the law in the state of Missouri is quite clear - you must stop before the light turns red or completely exit the intersection. You ran a yellow light."
He glanced at my driver's license. "You say you're from Edmonton, Canada - I can't imagine the rules are any different there on something as simple as this."
To say that the officer's face was hewn from granite would be unduly complimentary. My plea that I was out of state, heck - out of country - was, out of luck!
Then a flash of insight. I'd try physics!
"Actually, officer, I was in what could be called a dilemma zone. For some distances you can't stop legally even if you are going the speed limit. You know, that split second when you have to decide but you're too close to stop and too far away to make it through."
"The only dilemma I see here is whether you want to wait around till Monday to tell that pile of you know what to the judge."
For a brief moment a head-line played across my imagination "Two physicists shot dead in desperate bid to escape traffic violation - streets safe once again!"
"No, really officer. Look." I grabbed a pen from my coat pocket and a scrap of paper from the floor of the car. Dr. Bounder grunted and shifted a bit in the back. "Now, lets say I was 20 meters from the intersection and "
"What's a meter?"

3. I was tempted to say 106 microns but instead, meekly replied, "about three feet."
"You weren't 60 feet from the intersection, more like 80."
"Well, lets suppose I was 60 feet away just for the sake of argument. Now, if I was going 50 km/h then"
I glanced up at the officer. What's a kilometer - I know, I know.
"I mean, suppose I was going 30 miles per hour, then "
"I had you on radar, you were doing 28 miles per hour."
"But suppose I was going 30 miles per hour."
"Suppose I was the president!"
The non sequitur caught me off guard.
"But officer," I protested, "just for the sake of argument ..."
To a bystander I must have seemed a man possessed. For the next five minutes or so I waved my hands, scribbled numbers and drew graphs. At one point I even extracted a chuckle (it sounded like a chuckle) from the otherwise stolid protector of the peace and upholder of the sanctity of intersections.
Then, miraculously the officer relaxed, put his hand on the top of the car and said, "Edmonton, now I know - that's were that great big mall or whatever is? My cousin went there last year - wouldn’t stop talking about it!”
I couldn't bring myself to divulge the little known fact that I loathed and avoided aforesaid “temple of consumerism” with a passion so I meekly nodded and offered “same place."

4. "Look, seeing how you're out of state let’s just let you off with a warning. Drive carefully sir."
At this the officer snapped his traffic book shut with a sharp thwack, and waved me on.
Bounder grunted again and shifted to his other side, still oblivious to all in the back. As I glanced into the rear-view mirror, the small Missouri town was fading from sight. A feeling of satisfaction infused my being. Once again rationality, guided by the skillful application of physics had won the day!

5. The Problem
Your group must decide if my defense - that there are dilemma zones is - at least in principle - a reasonable one. To do this you must consider the following:
what physics is appropriate to this problem
what the essential problem in fact is
how you can best communicate your solution to others
what important pieces of information you would need to know in order to investigate the problem of dilemma zones

6. Have you ever...
Approached an intersection when the light changed from green to yellow and:
knew you couldn’t stop
knew there was no-way that you could make it through
Are there real “dilemma” zones in all or some intersections?

7. Do Dilemma Zones Exist?
What condition would tell us whether or not dilemma zones really do happen?
I don’t know what to do! I’m too close to stop and too far away to get through - YIKES!

8. Negotiating an Intersection...
There are two scenarios we must consider:
stopping safely
making it through safely

9. Safe Stopping... Parameters that will affect this:
maximum rate of deceleration (ad)
reaction time (tR)
Variables to consider:
initial speed of car (vi)
distance from the intersection
Put this into EXCEL

10. Safe “Going-For-It”... Parameters that will affect this:
maximum rate of acceleration (a)
reaction time (tR)
duration of yellow light (tY)
length of car (L)
width of intersection (W)
Variables to consider:
initial speed of car (vi)
distance from the intersection
Put this into EXCEL