$\"\"$

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The pilot’s final heading of $\"\"$ miles per hour in a direction of due west.

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The resultant velocity can be represented by vector $\"\"$ The resultant velocity is the sum of the vector representing the initial course $\"\"$ plotted by the pilot and the vector representing the wind $\"\"$ .

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Thus, $\"\"$ .

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Vector representing the wind $\"\"$ .

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The wind is blowing from the directed angle of $\"\"$ with a velocity $\"\"$ miles per hour.

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Draw the figure for the situation.

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$\"\"$

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Observe the figure, the wind is blowing at an angle of $\"\"$ with the horizontal.

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Component form of a vector $\"\"$ is $\"\"$ .

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Here $\"\"$ .

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Magnitude of the wind $\"\"$ is $\"\"$ .

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$\"\"$

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Substitute above result in $\"\"$ .

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$\"\"$

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Find the magnitude of $\"\"$ .

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$\"\"$

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$\"\"$

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Direction and the speed the pilot should set to achieve this resultant is $\"\"$ .

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$\"\"$

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Since $\"\"$ lies in the third quadrant, then $\"\"$ .

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Thus, the pilot needs to plot a course of about $\"\"$ miles per hour at a directed angle of $\"\"$ .

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$\"\"$

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Pilot needs to plot a course of about $\"\"$ miles per hour at a directed angle of $\"\"$ .