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6 August, 23:38

Problem 1: Problem 1.58 in Young & Freedman A plane leaves the airport in Galisteo and flies 170 km at 68.0° east of north; then it changes direction to fly 230 km at 36.0° south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, in which direction and how far should this crew fly to go directly to this plane?

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  1. 6 August, 23:50
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    We shall convert the displacement in vector form using unit vector i and j

    consider east as x axis and north as y axis

    170 km at 68.0° east of north

    D₁ = 170 sin68 i + 170cos 68 j

    = 157 i + 63.68 j

    230 km at 36.0° south of east

    D₂ = 230 cos36 i - 230 sin 36 j

    = 186 i - 135.2 j

    Resultant Displacement = D₁ + D₂

    = 157 i + 63.68 j + 186 i - 135.2 j

    = 343 i - 71.52 j

    Resultant magnitude

    = √ (343² + 71.52²

    = 350 km

    Angle

    = tan⁻¹ ( - 71.52 / 343)

    12⁰ south of east.
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