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10 September, 19:30

A speed boat travels with a speed of 6 m/s travels directly north to cross a river flowing west with a current traveling at a speed of 3 m/s. What is the resultant velocity of the boat?

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  1. 10 September, 19:51
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    6.7 m/s @ 116.6°

    Explanation:

    Use Pythagorean theorem to find the magnitude:

    v² = vx² + vy²

    v² = (-3 m/s) ² + (6 m/s) ²

    v = √45 m/s

    v ≈ 6.7 m/s

    Use trigonometry to find the direction:

    θ = atan (vy / vx)

    θ = atan (6 m/s / - 3 m/s)

    θ = atan (-2)

    θ ≈ 116.6° from the + x axis, or 63.4° north of west.
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