Help with a trig word problem!?

March 11th, 2010
  • A pilot attempts to fly her plane due east but a 72 mile per hour wind from the southwest blows the plane to a new course. If the airplane can do 285 miles per hour in still air, find the direction and ground speed of the plane on its new course.

    please help i cant get it. "/


  • Hi there Mysterious!

    ANSWER:
    Resultant Speed:
    339.748 miles per hour
    Direction: E 8.61 N

    SOLUTION: TWO WAYS!
    Here are two ways of doing it - will impress your lecturer/teacher!! :)

    METHOD 1: USING TRIGONOMETRY
    Use the cosine rule after drawing a diagram of the triangle:
    Ground Speed of Plane= sqrt (72^2 + 285^2 - 2(72)(285)cos135)
    ------------------------------------
    = 339.748 miles per hour
    ------------------------------------
    Now to get the resultant angle:
    Use sine rule:
    sinx/72 = sin135/340.7 ----> sinx = 0.1494---->x=8.6
    --------------------------------------...
    Resultant Angle: E 8.6 N (8.6 degrees North of Due East
    --------------------------------------...


    METHOD 2: USING VECTORS!
    Flying due east at 285 means:
    Plane Vector = 285i + 0j
    Wind from south west is moving in a north east direction, magnitude 72 = 娄ai + bj娄
    Magnitude = sqrt(a^2 + b^2) = 72
    North east is at 45 degree angle, so a = b
    Magnitude = sqrt(2a^2) = 72
    So a = b = sqrt(72^2)/2
    Wind Vector = 50.911i + 50.911j
    Resultant vector = Wind vector + plane vector

    (285 + 50.911)i + 50.911j
    335.911i +50.911j
    Resultant Speed = Magnitude = sqrt(335.911^2 + 50.911^2)
    -----------------------------------
    = 339.748 miles per hour
    -----------------------------------
    direction = tan -1 (50.911/335.911)
    --------------------------------------...
    = 8.61 degrees North of Due east!
    --------------------------------------...
    Hope this helps!

    p.s. The guy below has the final angle wrong! It should be North of Due East - Not East of Due North!


  • Draw a diagram, use cosine rule
    ground speed = sqrt [72^2 + 286^2 - 2(72)(286)cos135] = 340.7 miles/h
    use sine rule
    sinx/72 = sin135/340.7 ----> sinx = 0.1494---->x=8.6
    hence, direction = N81.4 E







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