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Components of unit vectors

  1. Mar 18, 2010 #1
    1. The problem statement, all variables and given/known data

    A golfer takes three putts to get the ball into the hole of a level putting green. The first putt displaces the ball 2.5 m North, the second 4.8 m South-East and the third 5.7 m South-West.

    Express each of these three displacements in unit vector notation where i is a unit vector pointing due East and j is a unit vector pointing due North.

    E.g the first displacement is: [tex](0)i, (2.5)j[/tex]

    3. The attempt at a solution

    The first one is obvious but the other two aren't. For example for the second part the question says it is 4.8 m South-East BUT it doesn't say how many degrees due South-East. Without the angle, it is impossible for me to find the rectangular components (i.e [tex]4.8 sin(\theta), 4.8 cos(\theta)[/tex]). Any suggestions?
     
  2. jcsd
  3. Mar 18, 2010 #2

    rl.bhat

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    When they say south of east or south of west the angle is always 45 degrees with east-west line.
     
  4. Mar 20, 2010 #3
    Oh thanks! I found the three displacements in unit vector notation:

    [tex]0i, 2.5j[/tex]
    [tex]3.39i, -3.39j[/tex]
    [tex]-4.03i, -4.03j[/tex]

    The question then asks:

    Determine the angle in degrees (measured with respect to anticlockwise rotation from an axis pointing due East of the hole) to get the ball into the hole in a single putt.

    What do I need to do to answer this problem? I'm a little confused...
     
  5. Mar 20, 2010 #4

    rl.bhat

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    Find the resultant of these three vectors.
    Then tanθ = y/x
     
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