Speed of wind and speed with respect to wind

  • Thread starter Astraithious
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In summary, the pilot is pointing the aircraft due west while the wind blows towards the NNE (67.5 degrees north of east). The resultant velocity of the aircraft over the ground is 64 m/s, 25 degrees north of west. Using the sine/cosine law, the speed of the wind is calculated to be 38 m/s, and the speed of the plane with respect to the wind is 85 m/s. However, it is possible that the official answers are incorrect as the wind speed should be lower than the plane's speed with respect to the wind.
  • #1
Astraithious
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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
 
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  • #2
What do the subscripts on v mean in your notation? And have you learned how to use vectors in i,j,k form?
 
  • #3
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
I don't think the definitions you have given are correct.
 
  • #5
Astraithious said:

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.
 

1. What is the speed of the wind?

The speed of the wind refers to how fast air is moving in a particular direction. It is typically measured in miles per hour (mph) or kilometers per hour (km/h).

2. How is the speed of wind measured?

The speed of wind is measured using an instrument called an anemometer. This device has cups that rotate when the wind blows, and the rotation is converted into a measurement of wind speed.

3. What factors affect the speed of wind?

The speed of wind can be affected by various factors such as temperature, air pressure, topography, and proximity to large bodies of water. These factors can cause changes in air pressure and temperature, which in turn impact the movement of air and the speed of wind.

4. What is the difference between speed of wind and speed with respect to wind?

The speed of wind refers to the absolute speed at which air is moving, while the speed with respect to wind refers to the speed of an object in relation to the speed of wind. For example, a person running with the wind at their back will have a higher speed with respect to wind compared to someone running against the wind.

5. How does wind speed affect weather patterns?

Wind speed is a crucial factor in determining weather patterns. Higher wind speeds can lead to more intense storms and can also affect the direction of weather systems. Wind speed also plays a role in influencing temperature and humidity, which are key elements in predicting weather conditions.

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