Thread: Bearing of wind

A plane, whose speed in still air is 500 km/h, flies from a point A to a point B, 1560km due north of A. Because of the action of a constant wind, the plane must head in a direction whose bearing is 009 degrees. Given that the flight takes 3 hours,
(i) Show that the speed of the wind is approximately 82.5km/h
(ii) Find the bearing of the direction from which the wind is blowing.

On another occasion the wind, whose speed is now 90km/h, is blowing from a direction whose bearing is 120 degrees. A second plane, whose speed in still air is 375 km/h, flies from A to a point C which is due east of A. Given that this flight also takes 3 hours.
(iii) find the distance AC

Part (i) is easy, but I have difficulty solving part (ii), can anyone help?
Also, for part (iii), the bearing of the wind is 120 degrees, i can't draw the diagram, where is the angle 120 degrees??bearing of vector?
I understand bearing of a fixed point from another fixed point, but bearing of a vector, i'm confused

Thanks

Are there no typos in your posted question?
Bearing 009 degrees? What is that? Is that the same as bearing 9 degrees?

Bearing 9 degrees is North 9deg East.
Bearing is measured from the North axis, going clockwise.

Hello, acc100jt!

A plane, whose speed in still air is 500 km/h,
flies from a point A to a point B, 1560 km due north of A.
Because of a constant wind, the plane must head in a direction whose bearing is 9°.
Given that the flight takes 3 hours,
(i) Show that the speed of the wind is approximately 82.5 km/h
(ii) Find the bearing of the direction from which the wind is blowing.

Code:

    B *
      | *  3w
      |   *
      |     *
      |      * C
 1560 |     *
      |    *
      |   * 1500
      |9°*
      | *
      |*
    A *

The plane intends to fly from to : km.

It must fly to , km, due to the wind.

Let = wind speed (in km/hr).
The wind blows from to in 3 hours:

Law of Cosines: .

Hence: .


Law of Cosines: .

Hence: .

Therefore, the wind is blowing from a direction
. . with a bearing of

On another occasion the wind, whose speed is now 90 km/h,
is blowing from a direction whose bearing is 120°.
A second plane, whose speed in still air is 375 km/h,
flies from A to a point C, which is due east of A.
Given that this flight also takes 3 hours.
(iii) find the distance AC

Code:

                              D
                              *     :
                          *    *    :
               1125   *         *60°:
                  *          270 *  :
              *                   * :
          *                    30° *:
    A * * * * * * * * * * * * * * * * C

The plane intends to fly from to
Due to the wind, it flies to : .

The wind blows from to : .

Law of Sines: .

Hence: .

. . Then: .


Law of Sines: .

Therefore: .