A plane, flying at 2000 km/h, wishes to reach a city 3000 km due East,
encounters wind blowing from N70W with speed 100 km/h.
(a) Find the velocity of the plane relative to the ground.
(b) How long will it take to reach the city?
2000t * : * 100t
* : *
o - - - - - - - - - - - o
A 3000 B
The plane intends to fly from to : . km.
The wind is blowing from D to B: .
. . Hence: .
Because of the wind, the plane flies from A to C at 2000 km/hr.
. . In hours, it flies 2000t km: .
In the same hours, the wind blows from C to B: . km.
In , Law of Cosines: .
This simplifies to: .
Quadratic Formula: .
. . which has the positive root: .
(b) The flight took 1.433 hours.
(a) The plane's speed was: .