1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Moreee vectors

  1. Sep 5, 2004 #1

    ios

    User Avatar

    A cross-country skier skis s1 in the direction theta1 west of south, then s2 in the direction theta2 north of east, and finally s3 in the direction theta3 south of west.

    How far is the skier from the starting point? I drew it..and it looks really really weird, I haven't done physics in a couple years now, and I'm a bit rusty, any help on how to start this?
     
  2. jcsd
  3. Sep 5, 2004 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I don't know how it could "look wierd"- that would depend on what the numbers involved are! In general, it is a zig-zag path.

    There are several different ways to do this. The way I would do it is to reduce to "components". Taking the positive x-component east and positive y-component n,
    The components of a vector "of length s in direction θ (measured from due e) would be < r cos(θ), r sin(θ)>. The only problem is the angles.

    If θ1 is "west of south" the angle measured from east is 270- θ1 and the vector is <s1cos(270-θ1), s1sin(270-θ1>.
    If θ2 is measured "north of east", then it is already correct. The vector is <s2cos(θ2),s2sin(θ2)>.
    If θ3 is measured "south of west", then we need to add 180 degrees to get the angle measured from east. The vector is <s3cos(θ3+ 180),s3sin(θ3+ 180)>

    Adding those components, the vector from the intial position to the final position is
    <s1cos(270-θ1)+s2cos(θ2)+s3cos(θ3+ 180), s1sin(270-θ1+s2sin(θ2)+s3sin(θ3+ 180)>

    To find the distance from the initial position to the final position, use the Pythagorean formula: square the two components, add and then take the square root.

    If you really are given only "s1, &theta;1", etc. then you will have a very complicated expression. If you are given specific numbers, substitute those first and then calculate.
     
  4. Sep 5, 2004 #3

    ios

    User Avatar

    i'm only given s1, theta1, s2, theta2, s3, theta3 :uhh:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Moreee vectors
Loading...