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Flying into a headwind

  1. Sep 16, 2011 #1
    1. The problem statement, all variables and given/known data

    The velocity of an airplane flying into a headwind is given by v(t) = 30(16 - t^2) mi/hr for 0 < t < 3 hr.
    How far has the airplane traveled at the instant its velocity reaches 400 mi/hr?

    Assume s(0) = 0

    3. The attempt at a solution

    I think I would have to find the area under the graph. So basically I have a velocity time graph? So my objective is to find the area under the graph between time 0 and the time where the plane reaches 400 mi/hr.

    I tried setting the velocity equation equal to 400 and solving for t, which would give me the time at which the velocity is 400 mi/hr, right? Well that didn't give me the answer that was in the book. What do you think?

    Thanks.
     
  2. jcsd
  3. Sep 16, 2011 #2

    Delphi51

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    Homework Helper

    The approach looks good. I get about 700 miles. I used integration to get the area accurately. If you would like a critique of your calc, share the details.
     
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