Question

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?

Answer 1

Answer:

$\theta=8.922714^{o}$ South-West direction

Explanation:

Let $V_{pa}$  be velocity of the plane relative to the air, $V_{ag}$  be velocity of the air relative to the ground, $V_{pg}$  is the velocity of the plane relative to the ground

therefore,

$V_{pg}=V_{pa}+V_{ag}$

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

$Sin \theta=\frac {V_{ag}}{V_{pa}}$

$\theta=sin^{-}\frac {38.0m/s}{245 m/s}$

$\theta=sin^{-1}0.155102$

$\theta=8.922714^{o}$  South-West direction