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Mechanics question derivations terminal velocity (quadratic case)

  1. Feb 21, 2014 #1
    hi so basically my question is derivation of derivation of the quadratic case of the terminal velocity


    I have attached the pictures in picture 1 I don't know I think the book has error in his derivation @ equation 2.4.13 shouldn't it be + instead of negative ??

    & in second picture their is something I don't understand two stuff acctually first is in equation 2.4.15
    how did he come up with 1/2 * dv^2 / dy? and my second question is
    du/dy = -1/vt^2 * dv^2/dy how did he come up with dv^2/dy ??

    thanks alot.
     

    Attached Files:

  2. jcsd
  3. Feb 21, 2014 #2

    maajdl

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    Gold Member

    Yes the sign is wrong.
    And dv/dt = dv/dy dy/dt = dv/dy v
    since v = dy/dt .
    And since dv²/dt = 2 v dv/dt, the last result follows.
     
  4. Feb 21, 2014 #3
    could u explain this line a little more ->dv²/dt = 2 v dv/dt, the last result follows?
     
  5. Feb 21, 2014 #4

    maajdl

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    Gold Member

    read:

    dv²/dy = 2 v dv/dy

    which implies

    v dv/dy = 1/2 dv²/dy
     
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