Airplane and Wind Vector question

In summary, an airplane is heading south at 500 km/h, and a southwest wind is blowing at 100 km/h. If the pilot does not take any corrective action, the plane will be off course by 9.36 degrees in 10 minutes.
  • #1
Avalonn
3
0

Homework Statement



An airplane is heading due south at a speed of 500 km/h. If a wind begins blowing from the southwest at a speed of 100 km/h, calculate the velocity of the plane relative to the ground, and how far off course it will be after 10 min. if the pilot takes no corrective action.

Answer: 435 km/h, 9.36 degrees east of south


Homework Equations



x = hypotenuse * cos(45)
x = 100 km/h * cos(45)

y = hypotenuse * sin(45)
Y = 100 km/h * sin(45)

The Attempt at a Solution



First I drew a diagram with N, E, S, W labeled. I then drew a line going NE since the wind is coming from SW. Then using the same starting point as the wind I drew 500 km/h going south to represent the airplane. I now wrote in a 45 degree angle for the wind. From this point I made a right triangle for the wind. To find the x and y I used sin and cos to get the values y = 70.71 km/h and x = 70.71 km/h. Am I on the right track or no?
 
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  • #2
Avalonn said:

Homework Statement



An airplane is heading due south at a speed of 500 km/h. If a wind begins blowing from the southwest at a speed of 100 km/h, calculate the velocity of the plane relative to the ground, and how far off course it will be after 10 min. if the pilot takes no corrective action.

Answer: 435 km/h, 9.36 degrees east of south


Homework Equations



x = hypotenuse * cos(45)
x = 100 km/h * cos(45)

y = hypotenuse * sin(45)
Y = 100 km/h * sin(45)

The Attempt at a Solution



First I drew a diagram with N, E, S, W labeled. I then drew a line going NE since the wind is coming from SW. Then using the same starting point as the wind I drew 500 km/h going south to represent the airplane. I now wrote in a 45 degree angle for the wind. From this point I made a right triangle for the wind. To find the x and y I used sin and cos to get the values y = 70.71 km/h and x = 70.71 km/h. Am I on the right track or no?

That's one good way to start. What next?
 
  • #3
I am stumped. Where do I go from here?
 
  • #4
After you get your velocity how do you find how the course of the plane movd in five minutes??
 
  • #5
I don't know. I never got a reply and ended up dropping the course without having to pay for it fortunately.
 

Related to Airplane and Wind Vector question

1. What is the meaning of "airplane and wind vector"?

"Airplane and wind vector" refers to the combination of the airplane's velocity vector (direction and magnitude of its motion) and the wind's velocity vector, which together determine the overall motion of the airplane through the air.

2. How does wind affect an airplane's flight?

Wind can affect an airplane's flight in several ways. If the wind is blowing in the same direction as the airplane, it can increase the airplane's ground speed and decrease its airspeed, resulting in a shorter flight time. However, if the wind is blowing in a different direction than the airplane, it can create turbulence and affect the airplane's stability, making it more difficult for the pilot to control the aircraft.

3. How do pilots account for wind when flying?

Pilots must constantly monitor wind speed and direction in order to make adjustments to their flight path and maintain control of the airplane. They use various instruments and techniques, such as windsocks, weather forecasts, and mathematical calculations, to determine the wind vector and make necessary adjustments to their flight plan.

4. What is the significance of the angle between the airplane's velocity vector and the wind vector?

The angle between the airplane's velocity vector and the wind vector is known as the wind correction angle. This angle is important because it determines the direction in which the airplane must be turned in order to compensate for the effects of the wind and maintain its desired course.

5. Can an airplane fly directly into a headwind?

Yes, an airplane can fly directly into a headwind. However, doing so will decrease the airplane's airspeed and increase its flight time. This is why pilots often try to avoid flying into headwinds and instead plan their flight path to take advantage of tailwinds, which can increase their speed and decrease their flight time.

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