A migrating salmon heads in the direction N 45° E, swimming at 5 mi/h relative to the water. The prevailing ocean currents flow due east at

Question

A migrating salmon heads in the direction N 45° E, swimming at 5 mi/h relative to the water. The prevailing ocean currents flow due east at 2 mi/h. Find the true velocity of the fish as a vector. (Assume that the i vector points east, and the j vector points north.)

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Thạch Thảo 4 years 2021-08-02T17:21:28+00:00 1 Answers 188 views 0

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  1. huyenthanh
    -1
    2021-08-02T17:22:47+00:00
    Reply

    Answer:

    Explanation:

    velocity of salmon with respect to water, v(s,w) = 5 mi/h at N 45° E

    velocity of water with respect to ground, v(w,g) = 2 mi/h due east

    Let the true velocity of salmon is velocity of salmon with respect to water is v(s,g)

    First write the velocities in vector from

    \overrightarrow{v}_{s,w}=5(Cos 45\widehat{i}+Sin 45\widehat{j})=3.54\widehat{i}+3.54\widehat{j}

    \overrightarrow{v}_{w,g}=2\widehat{i}

    Using the formula of relative speed,

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

    3.54\widehat{i}+3.54\widehat{j}=\overrightarrow{v}_{s,g}-2\widehat{i}

    \overrightarrow{v}_{s,g}=5.54\widehat{i}+3.54\widehat{j}

    This i the true velocity of salmon.

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