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23 August, 08:41

determine the magnitude and direction of the resultant for a combination of the vectors A: 10.1m, 60 degrees B: 7.3m, 275 degrees

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  1. 23 August, 09:33
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    5.87 m, 75.5°

    Explanation:

    Let's say C is the resultant vector.

    The x component is the sum of the x components of A and B.

    Cx = Ax + Bx

    Cx = 10.1 cos 60° + 7.3 cos 275°

    Cx = 5.69

    The y component is the sum of the y components of A and B.

    Cy = Ay + By

    Cy = 10.1 sin 60° + 7.3 sin 275°

    Cy = 1.47

    The magnitude is found with Pythagorean theorem, and the angle is found with trigonometry.

    C² = Cx² + Cy²

    C² = 5.69² + 1.47²

    C = 5.87

    θ = atan (Cy / Cx)

    θ = atan (5.69 / 1.47)

    θ = 75.5°
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