Flashbacks to the past: one of the first worksheets I published in this project was on using linear approximation to estimate the atmospheric pressure at various altitudes, and a later one was about a power function for atmospheric pressure. The derivation of the formula for atmospheric pressure is actually pretty straightforward. I'll assume that your students have not yet encountered integrals per se, but this worksheet pushes them to use their knowledge of differentiation to deduce an antiderivative.
This is a worksheet that puts together a few disparate concepts:
- dimensional analysis, using units to understand equations
- and baby differential equations.
It's certainly an activity for the end of the section on differentiation. The very last question asks students to think about a more accurate equation, and I wouldn't expect most students to be able to solve it alone -- but sometimes a good challenge is important as it points to concepts you'll be dealing with later on. Knowing how to integrate would really help in solving that last problem 🙂
As mentioned in the earlier posts, a great resource on atmospheric pressure and rocketry and all sorts of fun things is found at Portland State Aerospace Society's rocketry pages.