Q#11 (Past Exam Paper – June 2015 Paper 13 Q3 & March 2019 Paper 12 Q3)
The speed of an aircraft in still air is 200 km h-1. The wind blows from the west at a speed of 85.0 km h-1.
In which direction must the pilot steer the aircraft in order to fly due north?
A 23.0° east of north
B 23.0° west of north
C 25.2° east of north
D 25.2° west of north
Solution:
Answer: D.
For such a question, we need to properly identify the data we have, and what we are looking for.
With the wind blowing, it will cause the direction of the aeroplane to change during its motion. Due to this change, the pilot would need to steer in an appropriate direction in order to fly due north. Thus, the resultant of all our vectors should be in the north direction.
The wind is blowing from the west. So, the vector representing the wind would be horizontal.
The pilot of the aircraft would have to steer in a direction west of north in order to fly due north. Let the angle that the pilot needs to steer in order to fly due north (with the wind blowing) be at an angle θ west of the north.
The speed of the aeroplane is still 200 km h-1 – we are more interested with its direction.
The vector diagram below represents the situation.
The angle θ is given by 85.0 = 200 sin θ. {resolving the 200 km h-1 vector horizontally}
Angle θ = sin-1 (85/200) = 25.2°
So, the aeroplane needs to be travelling at an angle of 25.2° west due to north so that its resultant direction would be north when the wind blows.
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