A ship sets sail from Rotterdam, The Netherlands, intending to head due north at 6.5 m/s relative to the water. However, the local ocean cur

Question

A ship sets sail from Rotterdam, The Netherlands, intending to head due north at 6.5 m/s relative to the water. However, the local ocean current is 1.50 m/s in a direction 40.0º north of east and changes the ship’s intended motion. What is the velocity of the ship relative to the Earth?

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Euphemia 4 years 2021-08-20T09:46:26+00:00 1 Answers 10 views 0

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  1. thaiduong
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    2021-08-20T09:48:10+00:00
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    Answer:

    Explanation:

    velocity of ship with respect to water = 6.5 m/s due north

    \overrightarrow{v}_{s,w}=6.5 \widehat{j}

    velocity of water with respect to earth = 1.5 m/s at 40° north of east

    \overrightarrow{v}_{w,e}=1.5\left ( Cos40\widehat{i} +Sin40\widehat{j}\right)

    velocity of ship with respect to water = velocity of ship with respect to earth – velocity of water with respect to earth

    \overrightarrow{v}_{s,w} = \overrightarrow{v}_{s,e} - \overrightarrow{v}_{w,e}

    \overrightarrow{v}_{s,e} = 6.5 \widehat{j}- 1.5\left (Cos40\widehat{i} +Sin40\widehat{j} \right )

    \overrightarrow{v}_{s,e} = - 1.15 \widehat{i}+5.54\widehat{j}

    The magnitude of the velocity of ship relative to earth is \sqrt{1.15^{2}+5.54^{2}} = 5.66 m/s

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