Revisiting the basics

This week's post is

  • ┬áthe first this semester (fall semester! I am teaching again! I wasn't quite sure if I would or not!)
  • curiously appropriate, since I am up in the mountains this weekend.

I'm at Brian Head Resort briefly, running down a mountain. This running race starts at around 10,000 feet of elevation and I'm not used to it. There's a short initial uphill run, and then a chairlift ride, and then a lot of downhill. I am thinking keenly about the amount of oxygen available to my brain and muscles.

(I'm hearing from my running-mates that you can't drive a rental car up Mauna Kea -- they all die because the air is thin enough that combustion is affected. You've got to get a good SUV. So throw this out to your students as a real-life application!)

Regular readers might remember the first set of worksheets I did on altitude. As I come back to class this September I'm reminded that there's always room for working through the most basic concepts in a clear and straightforward way. The worksheet I'll post in a day or two (next internet access!) looks at the concepts around inverse functions: the horizontal and vertical line tests. It uses some data taken from empirical measurements of temperature at different altitudes. Remember that we're hot down here, the temperature drops as we climb mountains and fly up in planes, but then if we're on the sunny side of the planet the temperature rises again in the upper atmosphere. There are some wiggles in the middle, too. (Check out the graph at this site.) Clearly, me telling you what temperature I am does not tell you uniquely what altitude I'm at! On the other hand, pressure is monotonically decreasing as altitude increases, and so me telling you an atmospheric pressure would allow you to estimate my altitude.

More later: time to adjust to 10,000 feet!

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