I’m about to teach Related Rates in my Calculus class. And the book and the Internets aren’t helping me. Supposedly, related rates are so important because there are so many “real world” applications of it.
Like a snowball melting, a ladder falling, a balloon being blown up, a stone creating a circular ripple in a lake, or two people/boats/planes/animals moving away from each other at a right angle.
Weird exemplars — I wonder where they got started and why they still hold so much water in every textbook? Because seriously?!, a ladder sliding down a wall — when is anyone truly going to need to know the rate of change of the angle over time? Same with the melting snowball.
I’m not someone who needs a real world application to justify everything I teach. In fact, I rarely do. But when we’re teaching something and hold it up as “calculus in the real world,” I refuse to believe that this is the best we can come up with.
I am searching high and low for one true real world problem. No contrivances, but something where I can point to and say: “this calculation needed to get done and because it was, we now have ____.”
I am thinking that maybe figuring out how a radar gun calculates the speed of a car, especially if it is being used from a moving car, might have something good there.
So far, though, the closest I can get is here:
Rockets: A camera is mounted at a point so many feet from a rocket launching pad. The rocket rises vertically and the elevation of the camera needs to change at just the right rate to keep it in sight. In addition, the camera-to-rocket distance is changing constantly, which means the focusing mechanism will also have to change at just the right rate to keep the picture sharp. Related rates applications can be used to answer the focusing problem as well as the elevation problem.
A number of AP Calculus classes have their students make videos with related rates problems. But those problems are just like the others: contrived. It’s like using integration to do simple addition. This video is the exception; I love it.
Anyway, holla below in the comments if you got anything.