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Vector problem B

  1. Dec 5, 2003 #1
    A ship sails due east across lake at 19 mi/hr. The ship encounters a current flowing due northat 3.00 mi/hr

    A calculate the resultant velocity ( be sure to calculate the magnitude and direction)

    I drew a picture

    R^2 = 19^2 + 3^2
    R = about 19 mi/hr



    B) In what direction should the ship head in order to offswet the effect of the current
    tan-1 (3/19) = 8.97 degrees n of east

    Just need some reassurance I am doing these right
     
  2. jcsd
  3. Dec 5, 2003 #2
    First of all write vector eqn in terms of i,j,k components

    then apply
    [tex]V_a_b = V_a - V_b[/tex]

    rel velocity of a wrt b= vel of a - vel of b
     
  4. Dec 5, 2003 #3
    Always try to write vector eqn if you are not able understand graphically and derive the results accordingly
     
  5. Dec 5, 2003 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Two points:

    1) The problem said "calculate the resultant velocity " NOT "speed".
    Technically, velocity is a vector quantity.
    2) The problem specifically said " be sure to calculate the magnitude and direction"

    You have only given the resultant speed (magnitude of the velocity).

    You should either find the angle (arctan(3/19) north of east) or
    (much simpler) write the two given velocities as vectors and add:
    Using the standard convention that <1, 0> is east, <0, 1> north,
    19 m/h n is <0, 19> and 3 m/h e is <3, 0>

    The resultant velocity is <3, 19>. That was easy!
     
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