Our students in grades 4-7 at the Las Cruces Academy, our non-profit private school, enjoyed tracking the decolorization of phenolphtalein by hydroxide ion. Phenolphthalein is that beautiful rose-pink indicator dye used in acid-base titrations. It changes structure a bit in base but then slowly undergoes a permanent decolorization. The kinetics (rate and order of reaction) are interesting and fun to follow. **A write-up** from the 2018-19 school year is here.

## Falling skydiver

A skydiver jumps from a plane. How fast is he or she going at any time? There is a fairly simple expression for the drag on a body falling in air (“body” as a generic in the physics sense, not meaning “dead body!”). One can insert it into a simple differential equation that is “straightforward” to solve by separation of variables; along the way, I prove some useful relations. I also show how far off is the prediction of a simpler form often given for its simpler math.

## Model rocketry – equations and tests

Sort of a **one-stop-shop for model rocketry** theory, experiments, and data analysis for a high-school class, or an advanced middle-school class such as we have at the Las Cruces Academy:

Tsiolkovsky derived the equation for the final speed of a rocket in free space (no air drag) in 1903! I have a **derivation** here, plus an **elaboration** that goes on to consider air drag and gravity for a surface launch, and another one that looks at how a rocket **has to be designed** with propellant, payload, and basic infrastructure (the shell, we may say).

Our students at the **Las Cruces Academy** did rocket launches in the desert, measuring the altitude achieved with **geometric measurements**.

Some **pictures** are useful. Check out the link on the LCA News and Events page.

The **results** for altitude vs. rocket motor impulse are summarized in a spreadsheet. Altitude looks to be linear in impulse, in line with numerical **simulations** I performed. We had to be very careful with our measurements, btw, since **small errors** lead to big errors in altitude.

A sideline: **where does the kinetic energy go**, partitioned between exhaust gases and the rocket? At burnout for a serious rocket, there’s more in the gases than in the payload that’s left.