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"Wind" question

  • 19-02-2013 9:50am
    #1
    cmssjone
    Registered Users, Registered Users 2 Posts: 363 ✭✭


    Hi guys,

    Think I'm doing something a little stupid here as I can't seem to get this.

    I'm sure that u1 is correct:

    u1 = v + sqrt(2x^2-v^2)
    sqrt(2)

    For u2 I'm getting:

    u2 = v - sqrt(2x^2-v^2)
    sqrt(2)

    Can someone verify if I have u2 correct or not?

    Thanks


Comments

  • #2
    Yakuza
    Registered Users, Registered Users 2 Posts: 5,141 ✭✭✭Yakuza


    Try splitting v into i and j (horizontal and vertical) components (you really only want the i (horizontal) component). Hint : what is Cos 45 in terms of square roots?.

    On the outbound flight, the airplane's velocity in the direction of PQ will be x + the i component of the wind, on the way back it will be x - the i component of the wind.

    i) follows fairly quickly from the above
    ii) I actually get a different answer ([LATEX]x^2-\frac{v^2}{2}[/LATEX]), I might check my calcs later.

    In terms of the time taken to travel 2d (P to Q and back again), do you think the effect of the wind might cancel out over the two legs (given that it never changes speed or direction)?


  • #3
    cmssjone
    Registered Users, Registered Users 2 Posts: 363 ✭✭cmssjone


    Yakuza wrote: »
    Try splitting v into i and j (horizontal and vertical) components (you really only want the i (horizontal) component). Hint : what is Cos 45 in terms of square roots?.

    On the outbound flight, the airplane's velocity in the direction of PQ will be x + the i component of the wind, on the way back it will be x - the i component of the wind.

    i) follows fairly quickly from the above
    ii) I actually get a different answer ([LATEX]x^2-\frac{v^2}{2}[/LATEX]), I might check my calcs later.

    In terms of the time taken to travel 2d (P to Q and back again), do you think the effect of the wind might cancel out over the two legs (given that it never changes speed or direction)?

    Thanks for the quick reply Yakuza.

    Completely get the logic that regarding (i) with the wind aiding and hindering the plane your method is perfect so I am now wondering where I am going wrong with my calculations with my vector diagrams.

    I am positive that my calculation for u1 is correct (using the method of setting j = 0) and if I multiply u2 by -1 this provides the solution so maybe I have a sign error somewhere.

    I'll give it another go and post my calculations for scrutiny if I'm still not getting the answer.

    Thanks again!


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