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Falling object and air resistance

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data

    the effect of air resistance is to slow down a moving object. It can be shown that height of a falling object is given by the following

    2. Relevant equations

    y=y0-[t+(e^-bt - 1)/b]g/b

    a. show that for short times this reduces to the expected expression
    y=y0-1/2gt^2

    b. Find the velocity
    c. Find the acceleration
    3. The attempt at a solution

    I really not sure where to start with part a. what does it mean by reduces?
     
  2. jcsd
  3. Sep 27, 2009 #2

    Delphi51

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    Homework Helper

    You must replace the exponential with its power series. The power series will be a constant term plus a term with t, plus a t^2 term, plus a t^3 term and so on. For small times you can ignore the higher power terms. In this case keep only the first 3 terms.
    If you aren't familiar with power series, you can look them up in the back of the book or in a reference book with tables of integrals. The exponential one is also given here:
    http://en.wikipedia.org/wiki/Power_series
     
  4. Sep 27, 2009 #3
    Could you help explain how to find the velocity and the acceleration for the above equation. I know you differentiate it once for the velocity and then differentiate the velocity for the acceleration, but i'm having trouble.
     
  5. Sep 27, 2009 #4

    Delphi51

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    The expression for y is pretty ugly; I would expand it out like this:
    justin016.jpg
    Go ahead and try to find dy/dt. I'm sure you can do the constant terms and the one with a t factor. For the exponential, recall that the derivative of e^x is e^x.
     
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