Day 40 – A Cool Visualization of the Falling Ladder Problem

Ahhh, related rates. The classic ladder problem, which I find uninteresting for its “real worldliness” but kind of has a cool unintuitive aspect to it. If you pull away the bottom of the ladder at a constant rate, the top falls at an increasing rate. To see this, I got a bog tube (couldn't find a ladder) and put it against the wall. Then I had a kid put a sticky note at the top.then I pulled the bottom one square on the carpet way from the wall and had the kid put another sticky note at the top. We repeated this until the ladder hit the ground and then you can really visualize the top falling at an increasing rate (it looks weird from this angle, but is actually really easy to see from the front).

Then I had a WinPlot applet loaded of a ladder falling in a coordinate plane and had the students clap first whenever the bottom crossed a tick mark, and then when the top did. A great auditory way of realizing the same thing.

 

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2 responses to “Day 40 – A Cool Visualization of the Falling Ladder Problem

  1. Great idea for the ladder problem. I also love the unintuitiveness of the problem.

    However, I have a question about what else is in the picture. What is on your bulletin board about twitter?

    • It was a failed experiment but one I haven’t given up on! A few times I had my students write “Big idea tweets” to summarize particularly difficult conceptual lessons. And then some students elected to actually tweet them out. It was fun, but way too few students were interested. It still works well as a way to wrap up a lesson.

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