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physic

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An airplane flies due north at 200 km/h relative to the air. There is a wind blowing at 70 km/h to the northeast relative to the ground. What are the plane's speed and direction relative to the ground?

  • physic - ,

    v=200 km/h, v₀= 70 km/h,
    Angle that make v and v₀ is 45° =>
    An angle α in cosine law is
    α (360°-2•45°)/2 =135°
    Cosine law:
    V=sqrt(v²+v₀²-2vv₀cos α)=
    =sqrt[40000+4900-2•200•70•(-0.707)]=254 km/h
    Projections:
    x: v•cos90 +v₀cos45° =254cosβ
    y:vsin90+ v₀sin45°=254sinβ
    0.707•70 =254 cosβ
    200+0.707•70 = 254 sinβ
    49.49 =254 cosβ
    249.49 =254 sinβ
    sinβ/cosβ=tanβ =249.49/49.49 = 5.04
    β =tan⁻¹5.04 = 78.8° (northwest)

  • physic - ,

    Umm lol no

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