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Relative motion problem with airplane and wind velocity

  1. Feb 27, 2017 #1
    1. The problem statement, all variables and given/known data
    A small airplane wants to fly from A to B which is 200 km due south. The wind is blowing towards the east at a velocity of 50 km/h. If the airplane can move through the air at 300 km/h, find the direction the plane should be heading; the speed of the airplane relative to the ground; the time it will take to reach point B.

    2. Relevant equations
    p is plane, g is ground, w is wind
    Vpg = Vpw + Vwg

    3. The attempt at a solution
    I wrote out the givens to start:
    V = 300 km/h
    d = 200 km
    Vwg = 50 km/h [E]
    Vpg = ?

    I do not really know where to go from here. I understand that only one vector with both direction and magnitude is given (Vwg). The velocity of the plane is only a magnitude with no direction. I was unable to draw a vector diagram because I don't know what it should look like to accurately represent the scenario.
     
  2. jcsd
  3. Feb 27, 2017 #2
    So the wind is blowing from the West. The plane will need to fly at an angle west of south.
    If that angle is w, then the velocity south will be 300 cos(w) k/h and the velocity west will be 300 sin(w) k/h plus the speed of the wind (-50 k/h).
    So you need to make that east/west velocity zero and then work from there.
     
  4. Feb 27, 2017 #3
    I'm still unsure how to solve it; can you describe the next few steps please?
     
  5. Feb 27, 2017 #4
    Set up the equation for the east/west speed, set it to zero, then solve for cos(w).
     
  6. Feb 27, 2017 #5
    I got this equation: 300cos + 300sin - 50 = 0
     
  7. Feb 27, 2017 #6
    I got 300sin(w)-50 = 0
     
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