1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: An airplane in the wind

  1. Oct 14, 2008 #1
    1. The problem statement, all variables and given/known data

    An airplane is traveling at 30 m/s and wishes to travel to a point 8000 m NE (45 degrees). If there is a constant 10m/s wind blowing west:
    A) In what direction must the pilot aim the plane in degrees?
    B) How long will the trip take?

    2. Relevant equations

    Basic kinematic equations and trigonometry.

    3. The attempt at a solution

    Since I know only the magnitude of the velocity vector, and have to find the direction, I'm having trouble.

    I've tried taking the arcsin of 10/30 (Opposite over Hypotenuse) and got 19.47 degrees. Using the Law of Sines, I can calculate the other angles and the other side length.

    Side Length (m/s) Angle (Degrees)
    10 19.47
    30 58.4
    29.33 102

    Obviously, the 102 degrees doesn't make sense, since it is not opposite the largest side.

    Am I making this much more difficult than it really is?

    Please advise.
  2. jcsd
  3. Oct 14, 2008 #2


    User Avatar
    Homework Helper

    Likely you aren't making it difficult enough.

    What you do have is a vector addition. Except this one involves certain variables. I would recommend that you construct the vectors and their components, and then add them as you know they must be added to end at your destination.

    For instance let A be your wind speed blowing West. Withe East being positive X and H being the time to get there:

    [tex] \vec{A} = -10*H*\hat{x} [/tex]

    Likewise for the Plane:

    [tex] \vec{B} = 30*H*Cos \theta * \hat{x} + 30*H*Sin \theta *\hat{y} [/tex]

    And then you have your Destination vector:

    [tex] \vec{D} = 8000*Cos45*\hat{x} + 8000*Sin45 * \hat{y} [/tex]

    Since you know

    [tex] \vec{D} = \vec{A} + \vec{B} [/tex]

    Then solve for the angle.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook