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Free falling particle with air resistance

  1. Sep 5, 2012 #1
    1. The problem statement, all variables and given/known data

    A particle is release from rest (y=0) and falls under the influence of gravity and air resistance. Find the relationship between v and the distance of falling y when the air resistance is equal to (a) αv and (b) βv²

    3. The attempt at a solution

    Setting the origin at the point from where the particle is released, with y pointing downwards, we have, from F=ma, that dv/dt=g-αv, hence ∫dv=∫(g-αv)dt, so, as vdt=dy, v=gt-αy.

    Is it right so far? How do I eliminate the time depence? The solution manual has a very different approach that I did not understand, so it may be possible that my attempt won't get me to the answer. Thanks
     
  2. jcsd
  3. Sep 5, 2012 #2
    How can you represent dt in terms of dy and v?
     
  4. Sep 5, 2012 #3
    You indicate in the problem statement that air resistance (force) is alpha*v. Then you subtract it from g (gravity) which has different units and set it equal to acceleration. Your units do not jive.
     
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