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Most students taking physics have to be pretty smart.  The prerequisites for students in a college physics class include some amount of trigonometry, algebra, and, in many cases at least co-registration in the Calculus.

However, I was correcting labs the other day, and some of my students apparently believe that they were shooting small brass balls at speeds approaching 300 MPH!

Of course, they didn’t have this particular combination of number and units written down.  They did find the speed to be 133 m/s.  The problem is that students in the United States don’t have a feel for the metric system, so this number is essentially meaningless.  We tend to not know speeds in the metric system.

I’m not currently the instructor for the lecture section of this particular class, so I haven’t shared the following with my lab group, but I will be doing so today.  Maybe it will help you in your class.

Most people know that a reasonably fast “fastball” pitch is around 90 MPH, but only well trained athletes can throw a ball at this speed.

If we do a quick conversion, we can find the speed in meters per second.  (I’m using 1 mile = 1600 m instead of 1609 m to help keep the math simple.)

$$90 MPH=90 \frac{miles}{hour}\times\frac{1600 m}{1 mile}\times\frac{1 hour}{3600 sec}$$

$$90 MPH=90 \times\frac{16 m}{36 sec}$$

$$90 MPH=90 \times\frac{4 m}{9 sec}$$

$$90 MPH=10 \times\frac{4 m}{sec}$$

$$90 MPH=40 \frac{m}{sec}$$

So a 90 MPH fastball is travelling at about 40 m/s.

I like this number because students have a “feel” for the number.  It is too fast to drive on the highway.  It takes a lot of effort to throw a ball this fast.  No one would expect to shoot brass balls this fast in a crowded classroom.

The numbers are fairly easy to remember.  The derivation isn’t too hard to reproduce if a student doesn’t quite remember it.

Do you have any good markers for other quantities people should have a feel for in the metric system?