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

`\theta=8.922714^(o)` South-West direction

Step-by-step 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