Question

A plane flies on a heading of S60 degrees East at a constant speed of 550 km/h.
If the velocity of the wind is 50 km/h on a bearing of S40 degrees West, what is the velocity of the plane with respect to the ground?

Answer 1

the resultant velocity is just the sum of the two vectors. To get that, convert each vector to x- and y- coordinates, add them, then convert back to polar form.

Answer 2

That is if you know if the terminology means the wind is coming from the southwest or heading to the southwest. Bearing does not mean heading or direction of travel. I have no idea which it means. For me a SW wind means from the SW headed NE

Answer 3

v = 550(cos330,sin330) + 50(cos230,sin230)
= (476.3139..., -275) + (-32.1393..., -38.30222...)
= (444.17459..., -313.022..)

|v| = √(444.17459...^2 + (-313.022..)^2) = appr 543.55

or by cosine Law after making your sketch and using the diagonal of the parallelogram.
v^2 = 550^2 + 50^2 - 2(550)(50)cos80°
= 543.55..