A plane is heading on a bearing of 200° with an air speed of 400 km/h when it is blown off course by a wind of 100 km/h from the northeast. What is the resultant ground velocity of the plane?

Answer 1

We need to add two vectors:

400 km/k at a bearing of 200 degrees + 100 km/h at a bearing of 45 degrees

Decompose the vectors into their x and y components:

400 km/h @ 200 deg = 400 * sin(200) x + 400 * cos(200) = -136.8x - 375.9y

100 km/h @ 45 deg = 100 * sin(45) x + 100 * sin(45) = 70.7 x + 70.7y

Add them up

Total speed = -66.1 x - 305.2y

The length of the resulting vector is (66.1^2 + 305.2^2) = 312.3

The angle/heading is

180+ atan(66.1/305.2) = 180 + 12.2 degrees

Ground speed: 312.3 km/h @ 192.2 degrees