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27 June, 08:42

A man walks 600 m [E47°N], then 500 m [N38°W], then 300 m [W29°S], and finally 400 m [S13°E]. Find his resultant displacement.

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  1. 27 June, 08:50
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    The horizontal component of an angular distance can be calculated by multiplying the distance with the cosine of the angle, Dx = D * cos θ

    While the vertical component is calculated by multiplying the distance with the sine of the angle, Dy = D * sin θ

    The resultant displacement can then be obtained using the formula for hypotenuse and summations of each component:

    R^2 = (summation of Dx) ^2 + (summation of Dy) ^2

    summation of Dx = 600 * cos47 + 500 * cos128 + 300 * cos209 + 400 * cos (-77) = - 71.0372

    summation of Dy = 600 * sin47 + 500 * sin128 + 300 * sin209 + 400 * sin (-77) = 297.6267

    Note: you have to draw the lines to correctly determine the angles

    R^2 = (-71.0372) ^2 + 297.6267^2

    R = 306 m

    The resultant angle is:

    tan θ = Dy / Dx

    θ = tan^-1 (297.6267 / - 71.0372)

    θ = 103˚ = [N 13˚ W]

    Therefore displacement is 306 m [N 13˚ W].
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