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Homework Help: Tension on a Rope if used to Accelerate a car?

  1. Jul 27, 2007 #1
    1. The problem statement, all variables and given/known data

    A car is driven 100 km west and then 95 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)?

    ________ km
    ________ ° south of west

    2. Relevant equations

    none? I apologize if I am overlooking any equation, but there are no equations that I know of that can help when adding vectors. Perhaps the Pythagorean theorem in some cases.

    3. The attempt at a solution

    I really don't understand how to add this type of vector. Generally with vectors I separate them into their horizontal and vertical components, but in this case there is no angle given really..so I think that would be impossible. (Sine/Cosine won't work without an angle!)

    Thank you so much for your patience with me! I'm afraid I don't understand the concept very well...this is my first physics class, and my only knowledge of Physics is self-taught.
    Last edited: Jul 27, 2007
  2. jcsd
  3. Jul 27, 2007 #2
    You already have your components, east-west can be thought of as an x compoonent and north-south as a y component.
  4. Jul 27, 2007 #3
    Tension on a rope? Is that another question or something?

    Anyway, as far as vectors go, just think of them as triangles. For the first part the car is driven 100km west, so that is easy, and you can represent it as -100i (given that you make east and north positive). Then when the car drives 95 km southwest the car has a vector component that is west, and a vector component that is south.

    Looking at the second part as a triangle, you have the 95km southwest as the hypotenuse, and so the west and south parts will be the legs. The triangle has an angle of 45 degrees, since southwest is 45 degrees south of west (or you could at it as 45 degrees west of south). So if you use trigonometry then you will figure out what the length of the legs are. Hint: they should be equal, and one will point in the -i (west) direction while another points in the -j (south) direction.

    Add the like components, you have two that are pointed in the -i direction (west), and one pointed in the -j direction (south). Once you have the components added up you are back to having two legs. At this point I think you will see that this makes another triangle you can piece together with trig, and will be the triangle you are looking for.
  5. Jul 27, 2007 #4
    Sorry about the faulty title-I tried to go back and edit it after clicking "Submit" but the Edit Feature doesn't allow you to change the Subject Title

    Mindscrape: Thank you so much for your help! I didn't realize that "southwest" could be read as 45 degrees-I thought it was just a vague direction! (Sounds silly...I know.) I am indebted to your assitance! Thanks a ton! o:)
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