# Homework Help: Speed of wind and speed with respect to wind

1. Apr 22, 2015

### Astraithious

1. The problem statement, all variables and given/known data
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

2. Relevant equations
sine/cosine law

3. The attempt at a solution
i ended up with 85 for speed with respect for wind, and 38 for wind speed.

I just cant wrap my head around why they are swapped. Any help would be appreciated

2. Apr 22, 2015

### MarcusAgrippa

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

3. Apr 26, 2015

### 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

4. Apr 26, 2015

### MarcusAgrippa

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

5. Apr 26, 2015

### haruspex

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.