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The captain of a plane wishes to proceed due west. Thecruising speed of the plane is 245 m/s relative to the air. Aweather report indicates that a 38.0-m/s wind is blowing from thesouth to the north. In what direction, measured with respectto due west, should the pilot head the plane relative to theair?

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opudodennis

Answer:

[tex]\theta=8.922714^{o}[/tex] South-West direction

Explanation:

Let [tex]V_{pa}[/tex]  be velocity of the plane relative to the air, [tex]V_{ag}[/tex]  be velocity of the air relative to the ground, [tex]V_{pg}[/tex]  is the velocity of the plane relative to the ground

therefore,

[tex]V_{pg}=V_{pa}+V_{ag}[/tex]

From the triangle attached, the angle characteristics to the direction of relative velocity of the plane can be found

[tex]Sin \theta=\frac {V_{ag}}{V_{pa}}[/tex]

[tex]\theta=sin^{-}\frac {38.0m/s}{245 m/s}[/tex]

[tex]\theta=sin^{-1}0.155102[/tex]

[tex]\theta=8.922714^{o}[/tex]  South-West direction

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