We spent our spring school vacation in Washington DC. Enjoying the spring blossom, museums and monuments. On the way back we got “flashed” by a traffic camera at what seemed to be a rather slow speed on a very wide road. Two weeks later we received an interesting traffic ticket by mail. It claimed that we were driving at a speed of 46mph in a 35mph zone. Were we really? How does the camera knows? Prove it! Carefully reading this high tech traffic ticket, I realized how police are using some cool technology blended with math to create a convincing case... against us.
Speeding was detected by police radar that instructed a police camera to take two photographs of the speeding TheMathMom vehicle. The snapshots were taken with a time interval of 0.2 seconds, as the little stamp on the bottom shows. How do these pictures prove that we drove at 46 mph? Let's see...
If we drove at a speed of 46 mph, let's calculate how far we would move in these 0.2 seconds captured on the pictures.
speed = distance / time
from this:
distance = speed x time
distance = 46 mph x 0.2 sec
converting seconds into hours:
distance = 46 mph x 0.000055556 hours
multiplying, we get:
distance = 0.002555576 miles.
A very tiny number. Let's convert it to feet. I Googled that there are 5,280 feet in a mile. So, 0.002555576 miles would be 13.5 feet.
Ready for the final verdict? Did our car really move 13.5 feet in-between these two pictures?
Our traffic ticket explained that white marks on the road are painted with 5 foot intervals. I marked our car's back wheel positions on both snapshots with the red lines, observing that our car moved somewhere between 12 and 14 feet in-between these two pictures. 13.5 feet does, unfortunately, fit here very well, proving that we are guilty as charged. Oooof, I sometimes hate math!
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actually 35mph would be 10.2667 ft. Even if you were only doing 40.9 mph that would be 12 ft. The speeds are so low, its be hard to see with the road stripes how far you actually traveled (you would need an overhead shot to prove definitively) and if you sent in your calcs, they'd probably drop the charges.
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