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18 July, 07:18

A river flows due south with a speed of 1.4 m/s. you steer a motorboat across the river; your velocity relative to the water is 4.7 m/s due east. the river is 660 m wide. part a what is the magnitude of your velocity relative to the earth? express your answer with the appropriate units.

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  1. 18 July, 10:14
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    Refer to the diagram shown below.

    The river flow south at a velocity of 1.4 m/s.

    The motorboat moves east with velocity of 4.7 / s

    The velocity of the motorboat relative to the earth, v, is the vector sum of the two velocities. Its magnitude, by the Pythagorean theorem, is

    v = √ (4.4² + 1.4²)

    = 4.904 m/s

    Its direction south of east, is at an angle, θ, given by

    tan θ = 1.4/4.7 = 0.298

    θ = tan⁻¹ 0.298 = 16.6°

    Answer:

    The velocity of the motorboat is 4.9 m/s, at 16.6° south of east.
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