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Splitting a vector into two

  1. Apr 1, 2010 #1
    hello everybody
    can somebody help me how to do this exercise. i dont know how to start....
    a van is travelling north at a speed of 28m/s.after turning a corner it is heading 40° east of north at 25 m/s.
    work out the change in velocity of the van.

    first of all what i don't understand is what exactly do they mean with east of north? do they mean northeast?
    i tried to work out the resultant but thaats not possible as i cant use pythagoras as there's no right angle.

    i would be really happy to get some help
    thanks in advance :)
  2. jcsd
  3. Apr 1, 2010 #2


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    Homework Helper

    What does change mean? Surely not addition.

    40 degrees east of north means that you "rotate" your direction for 40 degrees east of north. :)
  4. Apr 1, 2010 #3
    Let's start off in polar coordinates assuming that north is in the direction of the positive y-axis and call the first velocity/angle V1 and the second V2.
    (in polar coordinates, an ordered pair is (r,theta) where r is the magnitude and theta is the angle)

    V1 = (28, 90)
    V2 = (25, 50)

    Now if you're looking for a simple change in velocity, it'd be 3m/s. But I'm guessing that'd be too easy. If you convert the polar coordinates to cartesian, then you can find the change in velocity with respect to y (north) and x (east).
  5. Apr 1, 2010 #4
    thanks for the explanation
    but i still dont understand it.
    whats a cartesian?
    in class we used to draw the vertical and horizontal component for such exercises.
    but i dont know how to apply it here
  6. Apr 1, 2010 #5
    i thought the change is 3 but that is apparently wrong:uhh:
  7. Apr 1, 2010 #6
    Draw a map with north on the vertical axis.
    The original velocity is 28 m/s in the vertical direction on the map.
    The speed after the change is 25 m/s, but the direction has also shifted to the right, forming a 40 degree angle with the original vector at the origin.

    What is the difference between those two vectors?
  8. Apr 2, 2010 #7
    is that right?
    28²+25² and then square root it?
  9. Apr 2, 2010 #8
    Not at all.
    1) The vectors form a 40 degree angle, not a 90 degree angle The Pythagorean theorem is useless here.
    2) The change is the difference between the vectors, not the sum--so even if the angle had been 90 degrees the Pythagorean theorem would be useless.
    3) The problem asks for change in velocity, not change in speed. The answer will be a vector, not a scalar.

    You need to learn how to subtract vectors, and you need to learn how to find the vertical and horizontal components of a diagonal vector (this will involve some trigonometry).

    Try drawing a diagram of the problem and see if that helps you understand better.
    Last edited: Apr 2, 2010
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