physics

A pilot wants the heading of an airplane to be 45º east of north. The wind is from 270º at 32 km/h, and the speed of the airplane through the air is 320 km/h. The pilot should maintain a heading of approximately?

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asked by kjean
  1. we want our east component to equal our north component so we get 45 degrees resultant. Wind is FROM 270, west.

    Heading or compass direction is clockwise from North

    wind is going 90 or East
    so our East speed is 320 sin(heading) + 32
    and our north component is 320 cos (heading)
    so
    320 sin heading + 32 = 320 cos heading

    sin heading + 0.1 = cos heading


    try some guesses

    heading = 10 deg
    left =.17+.1 = .27
    right = .98
    heading = 20 deg
    left = .34+.1 =.44
    right = .93
    heading = 30 deg
    left = .6
    right = .86
    heading = 40 deg
    left = .74
    right .76 really close !
    heading = 42 deg
    left = .77
    right= .74
    so between 40 and 42,
    heading = 41 deg
    left = .756
    right = .754
    Steer a compass heading of N 41 E

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    posted by Damon

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