Vectors

A plane is steering east at a speed of 240km/h. What is the ground speed of the plane if the wind is from the northwest at 65km/h. What is the plane's actual direction?

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  1. speed relative to ground: 240E+65*cos45E+65*sin45S
    combine like directions, then directionactual= arctan(S/E) south of East.

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    bobpursley
  2. resultant = 240(1,0) + 65(cos315, sin315)
    = (240,0) + (45.962, -45.962)
    = (285.962, -45.962)

    |resultant| = √(285.962^2 + (-45.962^2 )
    = 289.63 km/h
    angle: tanØ = -45.962 ÷ 285.962 = ....
    Ø = 350.9°°
    or S 80.9*° E

    or by cosine law:
    R^2 = 240^2 + 65^2 - 2(240)(65)cos135°
    = 83886.73..
    R = 289.63
    now use the Sine Law to find the angle

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