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Change in Velocity

  1. Jan 26, 2009 #1
    1. The problem statement, all variables and given/known data

    I am required to find the change in velocity given these two vectors:

    Va = 4.4 m/s [E31*S]
    Vb = 7.8 m/s [E25*N]

    2. Relevant equations

    delta V = Vb - Va
    delta V = Vb + (-Va)

    3. The attempt at a solution

    I am stuck between two solutions:

    #1. Simply subtracting the vectors:

    V = Vb - Va
    V = (7.8, 25*) - (4.4, 31*)
    V = [7.1, 3.3] - [3.8, 2.3]
    V = [3.3, 1.0]
    V = (3.5, 16.8*)

    #2. Reversing the direction of Va, its directionality becomes [W31*N], effectively 149*.

    V = Vb + (-Va)
    V = (7.8, 25*) + (4.4, 149*)
    V = [7.1, 3.3] + [-3.8, 2.3]
    V = (6.5, 59*)

    Which solution is correct and why? The first would solution would be the same if you distributed -1 across to both terms, but I'm pretty sure that operation is not permitted.
     
  2. jcsd
  3. Jan 26, 2009 #2

    LowlyPion

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    Doesn't taking the negative vector mean that the -31 is really 149 + 180 = 329
     
  4. Jan 26, 2009 #3
    Last edited: Jan 26, 2009
  5. Jan 26, 2009 #4

    LowlyPion

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    What is shown in your drawing is 329° and you are reversing it to 149° .
     
  6. Jan 26, 2009 #5
    Yes. Is that not correct, given that we are reversing the direction?

    Secondly, I have just drawn out a vector diagram to scale of the vectors in question. It seems to support #2, though I'm not sure how certain to be - given that I haven't work graphically with vectors in a while.
     
  7. Jan 26, 2009 #6

    LowlyPion

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    I believe Method 2 is the right way - the sum of the vector and the negative of a vector to do a vector subtraction..
     
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