On the old place, PEMDAS was the first word I blocked. And yes, if there is a way to say ambiguous things, the answer is not to argue (endlessly) about those statements when we could choose to make clear statements instead. This is also true in mathematics.

Yeah, this is appalling so many ways. But I hadn’t even considered the (likely?) possibility that my letters are now being used to train their AI. Can they do that without my consent , I wonder (as if I’ve been living under a rock)?

This is an amazing update to what was already superb!!! (And I will be studying it to try to learn how you did it! I tried and failed to add some of these enhancements on my own)

I wondered for a moment what work you were sending to the space station…Mr Aura indeed

I can’t disagree: we did this problem today!

Also, can I add that it is easy to write projectile problems that are way too hard, with challenging math but maybe not much more in physics understanding to be had.

I hope I don't "enforce" it either :) These are all style preferences, perhaps more useful for beginner problems. Still, I'd be curious to see an example of the kind of problem you are thinking of where the method is too constraining.

But I think I may see where you are coming from. Are you of the no-substitutions-until-all-algebra-is-finished school? If so, you are probably in the majority. I admit I am lax about that. So my students get away with solving for t and then substituting. That may be how we evade this issue

Well, okay. But the point is not to make doctrine but to encourage disciplined examination of each item. So given a launch speed of say 20 m/s at 30 degrees, I can ask: is that horizontal? No. Vertical? Still no. But it has components…

I make a chart that keeps horizontal and vertical separate but make a big deal that when either side of the chart hands you enough info to solve for time, you can “send that to the other side”. Is that what you are asking about?

We are not afraid!

Silly question: how are you measuring time? We started getting decent results when we switched to using phones. Now most groups are seeing errors of 5% or better. I can tell them that 30% is a measurement issue but say, 240% is a calculation error. Which mass spins? Which one hangs? 🤷‍♂️

Agreed! But many textbook proofs use the binomial thm approach which has the same flaw. Btw, logarithmic differentiation gets it all in one swoop but it comes later in the curriculum. Good thing pedagogy can stray from the sequencing demanded by the proofs :)

If the agreed convention is that .5 and greater rounds up, and if if we are interpreting “0.4999…” as a shorthand for the associated infinite sum, I think you have to round up. But it’s a fun question. It’s like, do you believe the math or not?

Have they posted the answer key yet?

It’s one of the great things about Desmos (and also about Interactive Physics) that it enables this kind of authoring almost on the fly. It becomes part of your teaching vocabulary. This one really shows that one thing!

Well, it’s languishing for a reason. It’s expensive and not web based. Barely supported any more. But it really does many cool things better than anything else I have seen.

It’s Interactive Physics, an under appreciated, languishing software package that is actually quite amazing. (This is my second grandpa post of the day)