Question

A high altitude jet airplane has a velocity relative to the air of 320 m/s due west. At a certain moment, the pilot notices a mountain peak directly west of

the plane at a horizontal distance of 4.20 km. 10 s later, the peak is observed to be a horizontal distance 4.18 km away in a direction 17?north of west.

(a) Set up a coordinate system and given the components of the displacement

vectors between the airplane and the mountain for both the initial and the final time.

(b) Use the information above to find the wind velocity.

Answer 1

This happened in 10 s so, assuming constant velocity, the south component of velocity of plane is 122 m/s relative to ground.
Since the plane is moving due west relative to air, then the only way for it to move south was for the air to move south at that speed.
Now,

Without the wind it would be 320 m/s, so that means the wind is blowing it back (east) at the speed of 320 - 20 = 300 m/s

Wind velocity = 300 m/s east + 122 m/s south.
(or)

324m/s 22.2° south of east.

Write Algebraically unit vector i point west and j south.

Solve this, You will get: