Question

The pilot of an aircraft wishes to fly due west in a 33.9 km/h wind blowing toward the south. The speed of the aircraft in the absence of a wind is 195 km/h. (a) In what direction should the aircraft head? (b) What should its speed relative to the ground be?

Answer 1

Answer:
`\theta =9.96^(\circ)` North of west

Step-by-step explanation:

Given

Plane wishes to fly in west

but wind with speed 33.9 km/h towards south obstructing its path

so plane must fly at an angle of \theta w.r.t west such that it final velocity is towards west

Plane absolute speed=195 km/h

To fly towards west velocity in Y direction should be zero

thus
`195sin\theta =33.9`

`\theta =9.96^(\circ)`

so Plane should head towards
`9.96^(\circ)` North of west in order to fly in west.

So plane

actual velocity is

`v=-195cos9.96\hat{i}+195sin9.96\hat{j}`