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Direction problem; find angle to shortest path with wind

  1. May 19, 2013 #1
    1. The problem statement, all variables and given/known data
    A pilot must travel directly to a town 500 miles away in a directions 20 degrees east of south from her present position. There is a steady 40 mph wind blowing west to east. Her plane's cruising speed through calm air is 95 mph. Using vector, what must be the plane's heading.


    2. Relevant equations
    tan-1(Ay/Ax) = angle of vector A.


    3. The attempt at a solution
    Vp/e = 95 mph south
    Va/e = 40 mph east
    Add vectors to get Vp/a = -95i + 40j → |Vp/a| = 103.078 mph
    Angle of Vp/a = tan-1(-95/40) = -67.2 degrees from...east? so 67.2 south of east.

    I feel like this is pretty far off, because I do anything with the fact the town is 500 miles away and 20 degrees east from south. Please help if you can :)
     
  2. jcsd
  3. May 19, 2013 #2

    tiny-tim

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    welcome to pf!

    hi caveman127! welcome to pf! :smile:
    no, Vp/a = 95 mph

    (and where did you get south from?)
     
  4. May 19, 2013 #3
    You might start by drawing a somewhat scaled vector diagram of this situation and you will see that 67.2 S of East is wrong. Also, I think that 103.078 is incorrect also. Once you get a good diagam, this is a trig problem.
     
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