To fight or not to fight (with the police....)

You know how I have been saying that math can be our friend, our tool and our weapon? Well, here is an interesting math role as a police persecution tool.

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!


Try it at Home:
Check out the new Try It at Home page from The Math Mom with a collection of tips and tricks to try at home.