What is the ground speed and heading of the jet measured from the west direction?

Question

A jet plane flying from Darwin, Australia has an air speed of 270m/s in a direction 5 degrees south of west. The plane is in the jet stream which is blowing at 35m/s in a direction 25 degrees south of east. What is the ground speed and heading of the jet measured from the west direction?

Answer 1

Here, you have 270cos 185° + 35cos 335° equal to -237.2517959.

Also, calculate 270sin 185° + 35sin 335° equal to -38.3236897.

Then take [(-237.2517959)² + (-38.3236897)²]^0.5 or 240.3271101 as

the magnitude of the resultant velocity vector.

The direction of the resultant velocity vector is given by the arctangent

of {-38.3236897 ÷ -237.2517959} which gives for Quadrant III (180 + 9.1758267)° 

or 189°10'32.98" in Degrees, Minutes, and Seconds.

The resultant velocity vector then amounts to 240.3271101 meters per second at

189°10'32.98"or 9°10'32.98" south of west.