Vectors Help - Word Problem?

A blimp is held in place with 2 ropes. Wind is creating a force of 300N on a bearing of 280 degrees, and one of the ropes is exerting a force of 250N on a bearing of 170 degrees. What force is being exerted by the other rope? 

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  • Pope
    Lv 7
    4 weeks ago

    This has been edited and corrected.

    Let w be the wind vector, and let u and v be the tension vectors. Break them up into components.

    w = 300sin(280°)i + 300cos(280°)j

    u = 250sin(170°)i + 250cos(170°)j

    u + v = -w

    v = -w - u

    v = -300sin(280°)i - 250sin(170°)i - 300cos(280°)j - 250cos(170°)j

    v ≈  252.0303i + 194.1075j

    Both components at positive, which places it in the northeast quadrant.

    r ≈ √(252.0303² + 194.10753²) ≈ 318.1 N

    θ ≈ tan⁻¹(252.0303 / 194.1075) ≈ 52.4°

    The missing tension vector is about 318.1 N, azimuth 52.4°.

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