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I don't know the exact english terms needed to write a proper question or perform a proper search, so here it is a detailed explanation of what I need: I have these expressions:

t = U * acosh(e^(h/(F*U)))

and

v = F*sqrt(1-e^((-2*g*h)/F^2))

I want to extract h from first and put it in second, so I get v expressed as a function of t.

I manually performed this calculation, but I'd like to have a "computer confirmation".

Is there any online or freeware tool capable of doing this?

I found this tool for inverse formula calculation: http://www.numberempire.com/inversefunctioncalculator.php Although it does not understand first equation, if I simplify it a bit, it eventually can handle it. But can't find anything to put h in second equation and get final expression for v.

jumpjack
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1 Answers1

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Go on wolfram alpha, type in the first equation, then write "solve for h", take what you get, sub it into the second one, put that in wolfram alpha and type something like "simplify" and see what happens.

Best

Ellya
  • 11,783
  • Nice, now I can't understand w'alpha response! ;-) What does it mean "cosh^(-2gU/F)" ???? – jumpjack Apr 01 '14 at 07:54
  • Would you mind posting its responses for both? – Ellya Apr 01 '14 at 08:18
  • T=Uacosh(e^(h/(FU))), solve for h gives – jumpjack Apr 01 '14 at 08:43
  • h= FUlog(cosh(t/U)) + something – jumpjack Apr 01 '14 at 08:44
  • v=Fsqrt(1-e^((-2g(FU*log(cosh(t/U))))/F^2)) gives – jumpjack Apr 01 '14 at 08:45
  • V=F*sqrt(1-cosh^(-2gU/F)(t/U)) – jumpjack Apr 01 '14 at 08:46
  • $$h=F U \log \left(\cosh \left(\frac{t}{U}\right)\right)$$ $$V=F \sqrt{1-\cosh ^{-\frac{2 g U}{F}}\left(\frac{t}{U}\right)}$$ are correct. What problem are you facing with Wolfram Alpha ? – Claude Leibovici Apr 01 '14 at 08:51
  • Idon't understand a bunch of things: 1) how do I add multiline comments here; 2) why I can't add comments at all from a Pc behind a firewall; 3) why on tablet I see "add/view 2 more comments", but link only works to add, not to show additional comments; 4) how do I write formulas as you did; 5) how do I write cosh^(-2gU/F) into WinPlot to plot it, or into excel: if cosh^-1() means acosh(),... what the hell does cosh^(-2gU/F) mean??? – jumpjack Apr 01 '14 at 10:15
  • Sounds like it's all worked out then, is that all okay? – Ellya Apr 02 '14 at 07:27