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Rearranging an equation

  1. Aug 29, 2010 #1
    I've got a kinematics equation modelling the flight of a stone:

    v = 10-gt
    s= -1/2 g t^2 +10t +2

    I can't remember how to get a value for v which doesn't contain t.
    I tried rearranging the first equation and introducing it to replace t in the second, but can't seem to get v isolated:

    (10-v)/g = t

    s = -1/2 g ((10-v)/g)^2 + 10((10-v)/g) + 2

    s = -1/2 ((10-v)^2/g) + (100-10v)/g + 2

    but I can't work out how to get a single expression for v. Can anybody help?
    This isn't a homework question, and I know the final solution is:
    v=sqrt(4g+100-2gs)
    It's just that I'm revising some stuff and really should know this already...!
     
  2. jcsd
  3. Aug 29, 2010 #2
    Try using conservation of energy:

    [tex]E=\frac{1}{2}mv^2+mgs=\textrm{initial value of E}[/tex]
     
  4. Aug 29, 2010 #3

    jtbell

    User Avatar

    Staff: Mentor

    It may not literally be a homework question, but it's a homework-like question, so it belongs here where it's been moved. :smile:

    It might be easier if instead of solving the first equation for t and substituting into the second equation, you do it the other way around: solve the second equation for t and...

    Do you remember how to solve a quadratic equation?
     
  5. Aug 29, 2010 #4
    Thanks for your reply.
    I realise that I can calculate this using energy considerations...but is there not a way to do it using algebra alone? I'm reading through a maths textbook that gives these equations and simply says "rearranging the equations we can easily show that..." then gives the solution. As the textbook doesn't presuppose any physics background, I was trying to work out how to do it algebraically without invoking any physics principles.
    Thanks
     
  6. Aug 29, 2010 #5
    Yes, sorry for posting in the wrong spot.

    I've got it now...just a momentary blank.
    Thanks for your help
     
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