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Difficult Velocity/Travel/Wind problem

  1. Mar 29, 2012 #1
    1. The problem statement, all variables and given/known data

    An aeroplane makes a round trip between two airports A and B located on the same line of longitude. On a windless day the aeroplane travels with constant speed v and the round trip time is T0. On the following day the same journey is made but there is a wind blowing at speed kv (k<1) at an angle z to the line AB. The pilot maintains the same speed v relative to the air and always flies along the line AB and BA. The round trip time is now T (neglecting take offs, landings and stopovers)

    Find T/T0

    2. Relevant equations
    See below

    3. The attempt at a solution

    I drew a vector diagram for velocity with v_r going horizontally(new speed along AB when there is wind) and the components v (plane speed) and kv (wind speed).

    I then used the cosine rule for v^2 = v_r^2 + (kv)^2 - (2 v_r kv cosθ)
    Solved for v_r to get:
    v_r = kvcosθ + v√(1-k2sinθ)

    Now, T/T0 = v/v_r ,
    so T/T0 = 1/(kvcosθ + v√(1-k2 sinθ))

    -----------------------------------------------------------------------
    The answer is given to be T/T0 = [(1-k2(sin2θ))0.5]/(1-k2)
    -----------------------------------------------------------------------

    I have tried to rearrange to get the same answer but I think I have gone wrong somewhere.

    Thanks for the help.
     
  2. jcsd
  3. Mar 29, 2012 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi Aaron7! :smile:
    (what does "r" stand for? :confused:)

    There are two trips, AB and BA, with different speeds. :wink:
     
  4. Mar 29, 2012 #3
    I got it :smile: Thanks for the help.
     
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