Displacement of airplanes in opposite directions.

In summary, the air traffic controller observes two airplanes approaching the airport and measures their displacements using vectors A and B. After breaking them into their components, it is found that the magnitude of vector C is 320km and it points 10 degrees north of west.
  • #1
321drought
4
0
An air traffic controller observes two airplanes approaching the airport. The displacement from the control tower to plane 1 is given by vector A, which has the magnitude 220km and points in a direction 32(degrees) north of west. The displacement from the control tower to plane 2 is given by the vector B, which has a magnitude of 140km and points 65(degrees) east of north. Find the magnitude and direction of vector C.

I understand that it needs to be broken up into its components, but I am unable to get the answer (320km @ 10(degrees) north of west). Thanks for any help.
 
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  • #2
321drought said:
Find the magnitude and direction of vector C.
What's vector C?
 
  • #3
C=A-B (the displacement from plane 2 to plane 1)
 
  • #4
321drought said:
C=A-B (the displacement from plane 2 to plane 1)
Good. So what are the components of A and B? (Call East +x, and North +y)
 
  • #5
Doc Al said:
Good. So what are the components of A and B? (Call East +x, and North +y)

Ax= (-220km)cos32
Ay= (220km)sin32
Bx= (140km)cos65
By=(140km)sin65
 
  • #6
321drought said:
Ax= (-220km)cos32
Ay= (220km)sin32
OK.
Bx= (140km)cos65
By=(140km)sin65
Careful: The angle here is given with respect to the North (y), not the East (x).
 
  • #7
Doc Al said:
Careful: The angle here is given with respect to the North (y), not the East (x).

Ahh yes, thank you! I have found the solution.
 

1. What is the principle of displacement of airplanes in opposite directions?

The principle of displacement of airplanes in opposite directions is based on Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. In this case, the two airplanes are creating an equal and opposite force on each other, causing them to displace in opposite directions.

2. How does the displacement of airplanes in opposite directions affect their flight paths?

The displacement of airplanes in opposite directions affects their flight paths by causing them to change direction. As the two airplanes push against each other, they will move away from each other in opposite directions, altering their original flight paths.

3. What factors can affect the displacement of airplanes in opposite directions?

The displacement of airplanes in opposite directions can be affected by various factors, such as the speed and direction of the airplanes, the weight and size of the airplanes, and the distance between them. Other factors may include wind speed and direction, air density, and atmospheric conditions.

4. Can the displacement of airplanes in opposite directions be controlled?

Yes, the displacement of airplanes in opposite directions can be controlled to some extent. Pilots can adjust the speed and direction of their airplanes, as well as maintain a safe distance from other airplanes, to minimize the effects of displacement. Air traffic controllers also play a crucial role in coordinating the flight paths of airplanes to avoid potential collisions.

5. Are there any safety concerns related to the displacement of airplanes in opposite directions?

Safety concerns can arise from the displacement of airplanes in opposite directions, especially if the airplanes are flying at high speeds or are too close to each other. In extreme cases, this displacement can lead to a loss of control or collisions between airplanes. Therefore, it is essential for pilots and air traffic controllers to be vigilant and follow safety protocols to prevent any potential accidents.

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