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20 May, 11:25

Luke is swimming in a river with a current flowing west to east at a constant speed of 3.5 meters/second. Assume that Luke's water speed is a constant 5 meters/second. If he tries to swim 60° east of north, his resultant speed is 2.63 6.58 7.40 8.22 8.52 meters/second and his direction angle is 17.70 35.82 71.63 103.01 144.18 °.

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  1. 20 May, 11:42
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    Decompose each velocity in its i and j - coordinates.

    1) River's velocity

    3.5 m/s, west fo east = 3.5i + 0j

    2) Luke's velocity

    5m/s, 60° east of north

    5 * sin (60°) i + 5*cos (60°) j = 4.33 i + 2.5 j

    3) Resultant velocity

    [3.5i + 0j] + [4.33i + 2.5j] = 7.83i + 2.5j

    resultant speed = √[ (7.83) ^2 + (2.5) ^2 ] = 8.22 m/s

    angle = arctan (2.5 / 7.83) = 17.7° north of east (equal to 72.3° east of north).
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