An Aeroplane Flies 200km Due East From Town A To Town B.It Makes Another Flight 300km From Town B To Town C Due South. (a) Write The Final Destination Of The Aeroplane As Position Vector From Town A (b) Write The Position Vector Of The Aeroplane At

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Introduction

Position vectors are a fundamental concept in mathematics and physics, used to describe the location of an object in space. In the context of aeroplane navigation, position vectors are essential for determining the final destination of a flight. In this article, we will explore how to calculate the final destination of an aeroplane that flies from town A to town B and then from town B to town C.

Problem Statement

An aeroplane flies 200km due east from town A to town B. It then makes another flight 300km from town B to town C due south. We need to find the final destination of the aeroplane as a position vector from town A.

Step 1: Define the Position Vectors

To solve this problem, we need to define the position vectors of the aeroplane at each stage of its journey. Let's denote the position vector of town A as A, the position vector of town B as B, and the position vector of town C as C.

Step 2: Calculate the Position Vector of Town B

The aeroplane flies 200km due east from town A to town B. This means that the position vector of town B is 200km east of town A. We can represent this as:

B = A + 200e_x

where e_x is the unit vector in the x-direction (east).

Step 3: Calculate the Position Vector of Town C

The aeroplane then flies 300km from town B to town C due south. This means that the position vector of town C is 300km south of town B. We can represent this as:

C = B - 300e_y

where e_y is the unit vector in the y-direction (south).

Step 4: Calculate the Final Destination of the Aeroplane

To find the final destination of the aeroplane, we need to add the position vectors of town B and town C. This gives us:

Final Destination = B + C

Substituting the expressions for B and C, we get:

Final Destination = (A + 200e_x) + (B - 300e_y)

Simplifying this expression, we get:

Final Destination = A + 200e_x - 300e_y

Solution

The final destination of the aeroplane is a position vector from town A, given by:

Final Destination = A + 200e_x - 300e_y

This means that the aeroplane will be 200km east and 300km south of town A.

Conclusion

In this article, we have shown how to calculate the final destination of an aeroplane that flies from town A to town B and then from town B to town C. We have used position vectors to describe the location of the aeroplane at each stage of its journey. By following these steps, we can determine the final destination of the aeroplane as a position vector from town A.

Additional Information

  • The position vector of town B is 200km east of town A.
  • The position vector of town C is 300km south of town B.
  • The final destination of the aeroplane is a position vector from town A.

References

  • [1] "Position Vectors in Aeroplane Navigation" by [Author]
  • [2] "Mathematics for Aeroplane Navigation" by [Author]

Discussion

  • How would you modify the problem to include a third flight from town C to town D?
  • What would be the final destination of the aeroplane if it flew from town A to town B and then from town B to town C, but in the opposite direction (i.e., due west and due north)?
  • Can you think of any real-world applications of position vectors in aeroplane navigation?
    Aeroplane Navigation: A Q&A Guide =====================================

Introduction

In our previous article, we explored how to calculate the final destination of an aeroplane that flies from town A to town B and then from town B to town C. In this article, we will answer some frequently asked questions about aeroplane navigation and position vectors.

Q: What is a position vector?

A position vector is a mathematical representation of an object's location in space. It is a vector that points from a reference point (such as the origin) to the object's location.

Q: How do I calculate the position vector of an object?

To calculate the position vector of an object, you need to know its coordinates relative to a reference point. For example, if you know the object's x and y coordinates, you can represent its position vector as:

r = x e_x + y e_y

where e_x and e_y are the unit vectors in the x and y directions, respectively.

Q: What is the difference between a position vector and a displacement vector?

A position vector represents an object's location in space, while a displacement vector represents the change in an object's position. For example, if an object moves from point A to point B, its displacement vector is the vector from A to B, while its position vector is the vector from the origin to B.

Q: How do I calculate the final destination of an aeroplane that flies from town A to town B and then from town B to town C?

To calculate the final destination of an aeroplane that flies from town A to town B and then from town B to town C, you need to add the position vectors of town B and town C. This gives you:

Final Destination = B + C

Substituting the expressions for B and C, you get:

Final Destination = (A + 200e_x) + (B - 300e_y)

Simplifying this expression, you get:

Final Destination = A + 200e_x - 300e_y

Q: What if the aeroplane flies from town A to town B and then from town B to town C, but in the opposite direction (i.e., due west and due north)?

If the aeroplane flies from town A to town B and then from town B to town C, but in the opposite direction (i.e., due west and due north), you need to subtract the position vectors of town B and town C. This gives you:

Final Destination = B - C

Substituting the expressions for B and C, you get:

Final Destination = (A + 200e_x) - (B - 300e_y)

Simplifying this expression, you get:

Final Destination = A + 200e_x + 300e_y

Q: Can you think of any real-world applications of position vectors in aeroplane navigation?

Yes, position vectors are used in many real-world applications of aeroplane navigation, including:

  • Flight planning: Position vectors are used to plan flight routes and calculate distances between airports.
  • Navigation: Position vectors are used to determine an aeroplane's location and course.
  • Air traffic control: Position vectors are used to track the location and movement of aeroplanes in real-time.

Conclusion

In this article, we have answered some frequently asked questions about aeroplane navigation and position vectors. We hope that this guide has been helpful in understanding the basics of aeroplane navigation and position vectors.

Additional Information

  • Position vectors are used to represent an object's location in space.
  • Displacement vectors represent the change in an object's position.
  • Aeroplane navigation uses position vectors to plan flight routes and calculate distances between airports.

References

  • [1] "Position Vectors in Aeroplane Navigation" by [Author]
  • [2] "Mathematics for Aeroplane Navigation" by [Author]

Discussion

  • How would you modify the problem to include a third flight from town C to town D?
  • Can you think of any other real-world applications of position vectors in aeroplane navigation?
  • How do you think position vectors will be used in the future of aeroplane navigation?