City Q lies 800km due north of city P. An aircraft has a speed of 450km h−1 relative to the surrounding air. A uniform wind of 80km h−1 blows from the west.
a. (i) In which direction (bearing with respect to the north) should the pilot head the aircraft so that it reaches city Q directly?
b. (ii) Find the ground speed of the aircraft under these conditions.
c. (iii) Determine the actual time of flight and comment on whether the aircraft can complete the journey in the scheduled 2h.