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Relative Velocity Airplane Problem - Air and Ground speed

  1. Jan 17, 2010 #1
    1. The problem statement, all variables and given/known data
    A jet flies with an airspeed of 310 mph due east (assuming +x is due east). It is climbing vertically with a velocity of 50 mph. A wind blowing toward northeast has a speed of 55 mph.

    2. Relevant equations

    Find the x,y,z components of the plane's velocity relative to the ground.

    3. The attempt at a solution

    Since nothing is affecting the z direction except the plane climbing, the z component would just be 50 mph.

    Because the wind is blowing toward the northeast, this adds a y component of
    (55 mph)*sin(45) =38.9 mph

    Both those answers are correct, but I am stuck on the x component.

    I tried adding 55mph*cos(45) to the 310 mph airspeed (since the plane is flying due east) to get 350 mph, but that is wrong.

    I also tried using the airspeed as the final vector's magnitude (i.e. x^2 + y^2 + z^2 = 310) using the correct answers above for y and z, but that is also wrong.

    Any help would be great.
  2. jcsd
  3. Jan 18, 2010 #2


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    What is the exact value of x component of the velocity?
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