Re: [Phys-L] simple Mathematica question (one more typo fixed)

[Francois Primeau <fprimeau@gmail.com>]

The problem is that Mathematica knows mathematics but not physics.  As stated, your problem is ill posed because you start it off at a point at which the derivative does not exist. Perhaps there is a way in Mathematica to start off your problem at y=100-epsilon for epsilon>0 and then take the limit as epsilon approaches zero.  
Best,
Francois 

Sent from my iPad

> On Dec 8, 2020, at 9:17 AM, Carl Mungan via Phys-l <phys-l@mail.phys-l.org> wrote:
>
> Since people seem to be in a talkative mood today, maybe somebody can help me a with a simple (?) matter. It involves dropping a rock. I’m using Mathematica but you don’t have to be an expert in that to see the issue.
>
> If we use conservation of mechanical energy, then we find the downward speed of the rock (choosing upward to be +y with the ground at y=0) is v_y = - Sqrt[2*g*(y0-y)].
>
> Suppose we choose y0 = 100 m and g = 9.8 m/s/s and ask Mathematica to do a numerical solution from t = 0 to 4 s:
>
> s = NDSolve[{y'[t] == -Sqrt[2 9.8 (100 - y[t])], y[0] == 100},   y, {t, 0, 4}]
>
> Plot[Evaluate[y[t] /. s], {t, 0, 4}]
>
> Can you guess what happens here? It’s a failure. The rock just sits at rest in the air at 100 m.
>
> If I instead start the evaluation at 99 m height, so the rock has already fallen 1 m, then it works just fine:
>
> s = NDSolve[{y'[t] == -Sqrt[2 9.8 (100 - y[t])], y[0] == 99},   y, {t, 0, 4}]
>
> Plot[Evaluate[y[t] /. s], {t, 0, 4}]
>
> But I want to start the rock at 100 m. How do I nudge the rock so it starts falling?
>
> I must be missing something. My actual problem is like this, but more complicated. The above is just a test case for debugging purposes.
>
> Who can tell me what I need to do? -Carl
>
> ps: Converting to acceleration does work but I don’t see why I should have to do that:
>
> s2 = NDSolve[{y''[t] == -9.8, y[0] == 100, y'[0] == 0}, y, {t, 0, 4}]
>
> Plot[Evaluate[y[t] /. s2], {t, 0, 4}]
>
> -----
> Carl E. Mungan, Professor of Physics  410-293-6680 (O) -3729 (F)
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