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: .