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: .