**Thursday, 20 February 2014**

You ever teach *that kid*, the one who has read ahead in his big sister’s calculus book, who’s forever watching Discovery channel on modern physics, who’s always asking for more detail than anyone else in class wants? Yeah, him. He’s a student in the classroom next door to mine. Yesterday, he swung by my room because his teacher had gone home for the day.

He brings me this:

The kid disagreed with his teacher but didn’t understand my colleague’s reasoning.

At this point, I think I’ve made some headway with the kid. He gets it physically, nothing can travel a finite distance in 0 time. But he’s still stuck on that function on his graph being f(x) = 1/x. So I bust my math teacher moves on him:

I’m convinced that math and physics teachers should talk more than they currently do. The only way I could think to explain this kid’s conceptual mistake (the asymptote is at y=0) was through both physical means (nothing can travel somewhere in 0 time) and correct his mistake was through mathematical means with a function transformation.

Oh, and yes, I really did write out that conversation after he left the room. It was too rewarding for me to forget.

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I love those 5 minute conversations with students on the tail end of a lunch/break! Some of the other physics teachers in my department complain incessantly about these kids, but for me one good physics conversation can make the whole day worthwhile, even if we don’t reach a solid conclusion.

Was he satisfied with your mysterious k? Is he familiar with N2? If so, you can still let him use his new-found knowledge of limits on an equation you derive for the time using N2, something like this:

∑F = ma (I’ll be using down → +)

mg – F_air = ma

a = (mg – F_air)/m

So the time of the drop is:

t = √(2Δy/a) = √(2Δy·m/(mg – F_air))

Then Lim(m→∞) t = √(2Δy/g) given that F_air has a max value at terminal velocity, and the graph has a nice horizontal asymptote exactly where you’d expect it to. I like https://www.desmos.com/calculator for graphing, just show him sqrt(x/(x-1)).

[Then challenge him to explain why the function is undefined between 0 and 1, and speculate on the negative-x side of the graph (negative mass? whoa!).]

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