Applications of mathematicsJason arrived several minutes late for our precalculus class with a smug grin on his face. It wasn't unusual for him to be late to class. It wasn't unusual to see him with a grin on his face. The combination, however, was decidedly peculiar. Jason's preferred mode of late arrival involved ducking into the back of the classroom as surreptitiously as possible, a rueful expression on his face to show he harbored dutiful feelings of guilt over his tardiness. This day, by contrast, he seemed quite pleased with himself.
He was so pleased with himself, in fact, that he could not resist sharing the explanation with me at the end of the period. The smile was still on his face when he sauntered up to the front of the room:
“Sorry I was late, Dr. Z. I got pulled over on my way to school.”
“Pulled over? Were you speeding?”
“Yeah, well, that's why I got pulled over, but the cop changed his mind.”
“That's a surprise. The CHP isn't known for backing off.”
“For sure true, but he had to. I used math to prove I wasn't speeding.”
“This I have got to hear. What happened, Jason?”
“Well, I was getting close to the freeway exit for the college when a black-and-white starting flashing red at me, so I pulled over. The patrolman came over and asked me if I knew how fast I was going, so I said, yeah, I was going at the limit. He started to tell me I was wrong, but I said, ‘I can prove it!’”
“This is going to be good,” I said to my student. “How on earth did you think you could do that?”
“I used the Pythagorean theorem and vector addition, of course. I told the cop that I was going exactly 55 miles per hour when he flashed me, but he thought I was going faster because I was also moving sideways toward the exit. I drew a speed diagram.”“You mean a velocity diagram.”
“Whatever. It was good enough for him. I showed him that he thought I was going too fast because he was looking at the long side of the triangle.”
“Hypotenuse.”
“Yeah, right. I said ‘hypotenuse,’ too. I think he was impressed. I told him it was unfair to ticket me for speeding when my forward motion was legal and that's what really counted. He started thinking about it and I asked him if it was okay if I ate some pizza and did he want some. I had takeout in my car to eat for lunch in the parking lot before class and it was just getting cold while we were sitting on the shoulder. He said, yeah, it was time for his lunch break anyway, so we sat there eating pizza and talking about math and speeding.”
I wasn't sure they really talked all that much about math, although I could believe that the patrolman was impressed by an excuse he probably hadn't heard before.
“So no ticket?”
“Yeah, no ticket! This math stuff can be useful! We got to talking and finished the pizza, so I didn't get to school when I expected. Sorry that made me late.”
He would have been late anyway, I'm sure, noshing on his pizza in the parking lot before class, but I was impressed by an excuse I hadn't heard before.
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3 comments:
Were those his exact numbers? If the speed limit was 55 and the officer thought he was going at 56, he would not have been stopped. Officers know that their radar has an error, so the rule is not to stop somebody unless the speed limit is surpassed by a certain minimum. (In Spain, this is 13%).
I don't recall that Jason actually told me any specific numbers. He may have just drawn a triangle for the patrolman and pointed out that the hypotenuse is longer. If they had fiddled with actually numbers, the CHP officer might have realized the extreme weakness of Jason's argument. For all I know, it was the pizza that clinched it.
I guess you didn't have the heart to tell him that his speed is actually the length of the hypotenuse, "the long side".
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