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Vectors Applications

  1. Jun 30, 2010 #1
    1. The problem statement, all variables and given/known data

    A pilot wishes to fly form city A to city B, a distance of 720 km on a bearing of 70 degrees. The speed of the plane is 700 km/h. An 60 km/h wind is blowing on a bearing of 110 degrees. What heading should the pilot take to reach his or her destination? How long will the trip take?

    2. Relevant equations
    Cartesian Vectors Equations

    3. The attempt at a solution
    I am not sure whether i did right

    First, alpha=90-70 degress=20 degrees
    Let a be the direction of the 2 cities.
    cos theta=cos 20=x/720
    sin theta=sin 20= y/720
    a=[720cos20, 720 sin 20]

    Let w be the direction of wind.
    110-90=20 degrees
    cos y=cos20=x/60
    siny = sin20=y/60
    w=[56.38, =20.52]

    let p be the vector of the plane

    |p|=sqre root of 732.96^2+225/73^2
    |p|= 766.93 km

    time = distance/speed
    =766.93km/700 km/h
    =1.10 h

    Since p=[732.96,224.73] we can use this info to find out the directional angle, B.
    tan B=225.73/732.96
    =17.12 degrees.
    90-17.12 =72.88 degrees

    The pilot should take the heading of 072.88 degree to reach his/her destination. It takes approx 1.10 hours.
  2. jcsd
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