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Vector components question

  1. Sep 25, 2013 #1
    1. The problem statement, all variables and given/known data

    A cyclist head due west on a straight road at 5.6m/s. A northeast wind is blowing at 10m/s. What is the effective speed of the tailwind?(resultant)

    2. Relevant equations
    Cos 45 10
    Sin 45 10



    3. The attempt at a solution
    Basically I broke it down into its x and y components. Then added them together to the Rx and Ry and used Pythagorean to find the resultant. I just have one question though: when adding the x components for the wind and the cyclist speed. Would the Rx be -5.6m/s + 7.1( 7.1 is derived from cos 45 degrees *10) = 1.5? Or would the 5.6 be positive?
     
  2. jcsd
  3. Sep 25, 2013 #2

    CAF123

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    Gold Member

    To help you answer your question, it might help to write out explicit expressions for the vectors representing the cyclist and the wind velocities.
     
  4. Sep 25, 2013 #3
    I did. Rx=ax+bx
    Ry=ay +by

    I'm just wondering since it's 5.6 m/s due west which on a Cartesian plane would be a negative x whether I would incorporate the negative when trying to find rx
     
  5. Sep 25, 2013 #4

    CAF123

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    Gold Member

    Yes, you can represent the velocity vector of the cyclist as ##\vec{C} = -5.6 \hat{x}## and that of the wind as ##\vec{W} = (10 \cos 45)\hat{x} + (10 \sin 45) \hat{y}##. Now, as you said, just add components to get the resultant.

    From a more conceptual point of view, imagine a game of tug of war. Person A pulls to left with force 5.6N and person B to right with force 10cos45 ≈ 7.1 N. The person pulling to right wins, but only marginally. (winning by 7.1 - 5.6, not 7.1 + 5.6)
     
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