Answer: about $50.
This problem was a little trickier than the previous six. Here, I show a couple of ways of approaching this problem. There are, of course, many valid ways to approach it.
First, there are three important pieces of information in the statement of the problem: your speed, the speed limit, and how much tickets cost for each mile per hour over the speed limit you were driving. Here they are in a list:
Your speed ........... 33.5 meters/second (m/s)
Speed Limit ......... 29.1 meters/second (m/s)
Tickets Cost ......... $5 per mile per hour (mph) over the speed limit
OK, so you know your speed, the speed limit, and how much tickets cost per mile per hour (mph) of excess speed. The first thing to do is to find out how much faster you were driving than you should have been: 33.5 m/s - 29.1 m/s = 4.4 m/s. So you were going 4.4 m/s over the speed limit.
Next, you need to convert the speed excess from m/s to mph. You need to do that because I gave you the fine in dollars per excess mph. Here's the conversion:
Here, I have used the fact that there are 1609 meters in a mile, 60 seconds in a minute, and 60 minutes in an hour. The conversion above is an example of dimensional analysis, which you can read more about in Handout 1, Section 3.
So, you were travelling 9.84 mph over the speed limit. Tickets cost $5 per mph over the speed limit, so the fine is 9.84 $5 = $49.20. So you owe the City of San Diego $49.20, or right around $50.
Another valid way to do the problem is shown below. You could also have converted your speed and the speed limit from m/s to mph at the beginning, like:
So your speed is 33.5 m/s (74.9 mph), and the speed limit is 29.1 m/s (65.1 mph). The difference in speed is about 10 mph. You again multiply by $5 to get the fine. Again, the answer is about $50.
Now, I was worried after I re-read the assignment, because I noticed a part of question 7 which was potentially ambiguous. I had written ``m/s'' for meters per second and ``mph'' for miles per hour. However, I didn't actually say that ``mph'' meant miles per hour -- it could have meant meters per hour. I decided that, if anyone had that problem, I would accept their answer as well (if they did the rest of the problem correctly).
Luckily, only one person had that trouble. For that person's benefit, here is how the problem works if you interpret ``mph'' to mean meters per hour. First, you need to convert your speed difference (4.4 m/s) into meters per hour:
After making this conversion, you have the speed difference in meters per hour. All you have to do next is multiply by $5 per meter per hour, and you get the fine -- $79,200! That's a pretty steep speeding ticket.