Photo Enforcement: Was Mr. Schuetz Speeding? Worksheet to accompany article appearing in The Physics Teacher, April 2008.
To the teacher: This document contains two different worksheets.
The first one is very much of a recipe, helping students in the process from one step to the other. Two pages total length.
The second version requires students to investigate the whole incident on their own, as if they had just received a ticket in the mail and wanted to verify the legitimacy of the infraction.
The answers: The car was going 58 mph This value can be seen in the original images in the lower left corner. This resulted in a $50 fine.
Students who are not careful and merely estimate 15 feet (three full stripes) will get a speed of about 51 mph, thus underestimating my fine. Students who are more careful and approximate 17 feet will get 58 mph.
Images on the worksheet and the website have the radar speed blotted out. The original images can be found here: http://schuetz.physics.googlepages.com/speeding2 Additional pictures from a second speeding “incident” also appear on the website. Have phun! Photo Enforcement: Was Mr. Schuetz Speeding?
The back story:
In May, 2006 Mr. Schuetz received a letter in the mail from the Washington DC Police Automated Speed Enforcement Program. Apparently in April he was speeding through a section of the district. In his defense, he had never been on that section of road before, and it sure looked like a highway to him. Nonetheless, the posted speed was 45 mph. The $100 question is, how fast was he going?
The details:
The radar that caught him speeding records about 250 measurements per second to measure the speed of the vehicle. So it is probably correct. But just to show us, the savvy consumer, that we were in fact speeding, there is a camera set up to record three images. One is a close up of the license plate. The second and third are pictures of the car as it is passing through a marked section of pavement. From the DC photo enforcement website you can learn all the details about the system http://mpdc.dc.gov/mpdc/cwp/view,q,548005,mpdcNav,|31886|.asp including: The images are recorded 0.2 seconds apart. The stripes on the road surface are 5 ft apart. The fines are progressive. The fine is $30 for 1–10 mph over, $50 for 11–15 mph over, $100 for 16–20 mph over, $150 for 21 to 25 mph over, and so on.
Your assignment:
Figure out how fast Mr. Schuetz was driving, and therefore, how big of a fine he should have received. To help in your measurements, you can see larger, full color versions of these images by going to this website: http://schuetz.physics.googlepages.com/speeding Questions:
1. What total distance (in feet) did the car travel from one photo to the next? It may be helpful to carefully mark the position of a tire in each photo on the stripes below. Each stripe is painted 5 feet apart on the roadway.
2. Knowing that the images are 0.2 seconds apart, show your work to calculate the speed of the car in ft/sec.
3. I don’t know about you, but my speedometer doesn’t show my speed in ft/sec. Show clear work in converting your answer into miles/hour. Recall that there are about 5280 feet in one mile.
4. If you did your measurements and calculations correctly, you should find that Mr. Schuetz was speeding. Make sure that your answer shows a reasonable speed for Mr. Schuetz’s car, and then determine how much of a fine he got.
5. Once you have calculated a speed for the car, ask your teacher for the actual speed as measured by the radar detector (this is the information blotted out on the lower corner of the image), and the actual fine that this speed would have received.
6. Calculate how far off you are (in percent) from the radar gun’s measurement:
Actual Measured Percent _ Error 100% Actual
7. Some of your classmates, and maybe even yourself, did all the math correct but predicted the wrong fine that Mr. Schuetz got. Discuss how this could occur, and what steps you could take to ensure that you correctly determine the speed. Washington DC Photo Enforcement Official Investigation
Mr. Schuetz, a mild mannered physics teacher, received an envelope in the mail one day from the Washington DC Metropolitan Police department, containing the following pictures, and a request for payment. The letter claimed that Mr. Schuetz was observed to be driving at excessive speed through a section of Washington DC where the speed limit is only 45 mph. You are tasked with using the information provided on these photos, and the information provided by the Washington DC Metropolitan Police Department to carefully investigate the legitimacy of the infraction, and determine what fine, if any, that Mr. Schuetz should pay.
To help you in the investigation, you can see full color, high resolution images of Mr. Schuetz’s car here: http://schuetz.physics.googlepages.com/speeding
Detailed information about how the photo enforcement system works, how fines are determined, and other important information can be found by visiting the Washington DC police website photo enforcement website: http://mpdc.dc.gov/mpdc/cwp (select the automated speed enforcement link from the left menu).
Your final report should contain all the information that you needed to gather, and all the calculations you needed to perform, in order to accurately determine the speed of Mr. Schuetz’s car. You should also be able to report what fine, if any, he should have received.