To calculate the direction the pilot must aim for in order to fly directly west, we can break down the velocity vectors of the plane and the crosswind:
Let's call the direction the pilot must aim for as θ.
The velocity of the plane in still air towards the west is 510 km/h.
The velocity of the crosswind from the south is 120 km/h.
We can set up a right-angled triangle using the velocities of the plane in still air, the crosswind, and the resultant velocity (which is the velocity of the plane relative to the ground).
The resultant velocity can be calculated using the Pythagorean theorem:
resultant velocity = sqrt((510 km/h)^2 + (120 km/h)^2)
resultant velocity = sqrt(260100 km^2/h^2 + 14400 km^2/h^2)
resultant velocity = sqrt(274500 km^2/h^2)
resultant velocity ≈ 524.1 km/h
Now we can calculate the angle θ using trigonometry:
tan(θ) = opposite/adjacent
tan(θ) = 120 km/h / 510 km/h
tan(θ) = 0.2353
θ = arctan(0.2353)
θ ≈ 13.2 degrees
Therefore, the pilot must aim for a direction of approximately 13.2 degrees north of west in order to fly directly west.
The velocity of an aeroplane in still air is 510 km/h. The plane flies due west but experiences a crosswind of 120 km/h from the south. Calculate: 6.1 The direction of the pilot must aim for in order to fly directly west
1 answer
2 answers