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Addition of Vectors Question

  1. Dec 16, 2011 #1
    1. The problem statement, all variables and given/known data

    I set out on a compass heading of 15.0 degrees west of south for 23.4km.

    I turn 20.5 degrees east of south and travel another 32.0km.

    What is my displacement?

    2. Relevant equations

    I'm not sure if there are any. But these should help.

    Ax = A cos θ
    Ay = A sin θ
    Bx = B cos θ
    By = B sin θ

    3. The attempt at a solution

    Alright, I'm not sure at all of this but:

    Ax = -23.4km cos 75 = -6.05
    Ay = -23.4 sin 75 = -22.6

    That's all I've come up with. Can someone tell me if I'm doing this right, and guide me through the process of finding a solution?

    Thanks in advance.
  2. jcsd
  3. Dec 16, 2011 #2


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    I believe you have the trig functions backwards. DRAW A DIAGRAM and that shall be confirmed one way or the other. [Actually I don't know why you are using 75 degrees]
    When you sketch the diagram, your 15 degree angle might not be exact - unless you use a protractor, but it should be a lot less than 45 degrees. Otherwise you will lose the guidance of your picture, and will have wasted your time drawing it in the first place.
  4. Dec 16, 2011 #3


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    Hello Scooter I. Welcome to PF !!

    These are correct !

    Do likewise for Bx & By .

    Then add like components together.
  5. Dec 17, 2011 #4
    Can anyone else verify that I'm doing it correctly...? I really don't think so.
  6. Dec 17, 2011 #5
    Ax and Ay seem correct to me.

    Do the same with Bx and By, Bx should be positive and By should be negative as you have defined North and East to be the positive directions.

    Add the components so you have a total x displacement and total y displacement, then use pythagoras theroem to find total distance.

    Edit: Also you're are asked to find displacement which is a vector quantity i assume you also need to find the angle as well as the distance. Oce you have found the total x displacement and total y displacement, you can work this you by drawing a triangle and using trigonometry.
    Last edited: Dec 17, 2011
  7. Dec 17, 2011 #6
    well in fact you just need the angle in between your vectors.

    |A+B|= SQRT( A^2 + B^2 + 2 cosθ AB)
    On the right side are the magnitudes and not vectors

    θ= 15.0 deg + 20.5deg .
    Because they are west and east the total angle you can find is the Thita1 of the vector 1 to South and Thita2 of the vector 2 to south.

    Now you put numbers and it's finished
  8. Dec 17, 2011 #7


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    Because you changed to 75 degrees, rather than using to the 15 degree angle given, you original expressions were correct.

    I hope you have drawn a diagram - if you have you would be more confident of any answers you calculate - by relating it to that diagram.
    Last edited: Dec 17, 2011
  9. Dec 18, 2011 #8
    Would B be: Bx = 32.0km
    By = 32.0km sin 75 = 30.9km

    And then the angle would be 17 degrees? But I don't know what direction.
  10. Dec 18, 2011 #9


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    Have you drawn a diagram yet? That will show you the direction!
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