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Simple newtons laws question ?

  1. Apr 16, 2012 #1
    "Simple" newtons laws question ?

    At time t = 0 a particle of unit mass is projected vertically upward with velocity v_0 against gravity, and the resistance of the air to the particle's motion is κ times its velocity.
    Show that during its flight the velocity v of the particle at time t is

    [tex] v = (v_0 +\frac{g}{k}) e^{-kt} - \frac{g}{k} [/tex]


    Now what I have done is work with newtons 2nd law:

    [tex] mx'' = -mκv [/tex]
    [tex] v' = -κv [/tex]

    solving this differential equation gives:

    [tex] v=Ce^{-kt} [/tex]

    Now v(0) = v_0 from question so:

    C=v_0

    [tex] v=v_0 e^{-kt} [/tex]

    Now clearly I missing quite a bit of stuff, so where exactly am I going wrong ?
     
  2. jcsd
  3. Apr 16, 2012 #2

    LCKurtz

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    Re: "Simple" newtons laws question ?

    You have left the force of gravity out of the differential equation.
     
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