Speed of wind and speed with respect to wind

[Astraithious]

Homework Statement

A pilot points an aircraft due west, while the wind blows towards the NNE (45 degrees north of east). The resultant velocity of the aircraft over the ground is 64 m/s, 25° N of W .

(a) At what speed does the wind blow, and

(b) what is the speed of the plane with respect to the wind? (7 marks)
a) Vpw = 85 m/s
b) Vwg = 38 m/s[/B]

Homework Equations

sine/cosine law

The Attempt at a Solution

i ended up with 85 for speed with respect for wind, and 38 for wind speed.

I just can't wrap my head around why they are swapped. Any help would be appreciated

 

[MarcusAgrippa]

What do the subscripts on v mean in your notation? And have you learned how to use vectors in i,j,k form?

 

[Astraithious]

Sorry for the late reply and no i have't yet. first is vpw = speed of wind and vwg is velocity of the plane with respect to the wind

 

[MarcusAgrippa]

I don't think the definitions you have given are correct.

 

[haruspex]

Homework Statement

A pilot points an aircraft due west, while the wind blows towards the NNE (45 degrees north of east). The resultant velocity of the aircraft over the ground is 64 m/s, 25° N of W .

(a) At what speed does the wind blow, and

(b) what is the speed of the plane with respect to the wind? (7 marks)
a) Vpw = 85 m/s
b) Vwg = 38 m/s[/B]

Homework Equations

sine/cosine law

The Attempt at a Solution

i ended up with 85 for speed with respect for wind, and 38 for wind speed.

I just can't wrap my head around why they are swapped. Any help would be appreciated

NNE is not 45 degrees N of E. That's NE. NNE is 67.5 degrees N of E.
Are you saying the two answers you quote are swapped around in relation to the official answers? If ao, the official answers must be wrong. The aircraft's course is not greatly affected by the wind, so the wind speed must be the lower of the two.
If you still have reason to think your answers are wrong, please post your working.