Adding Vectors. Help starting?

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In summary, the conversation discusses how to find the location of city C relative to the starting point of a commuter airplane's route, which includes stops at cities A and B. The method involves breaking down each vector into components using trigonometry and then adding them up to find the resultant value. The conversation also mentions the importance of keeping the signs straight for different directions.
  • #1
Kildars
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A commuter airplane starts from an airport and takes the route shown in Figure P3.17. It first flies to city A located at 227.5 km in a direction 30.0° north of east. Next, it flies 195 km 20.0° west of north to city B. Finally, it flies 247 km due west to city C. Find the location of city C relative to the location of the starting point.

A) km (distance from the starting point)
B) ° west of north (angle from the starting point)
sf_route.gif


I'm not asking for people to do it for me, just show me where to start -- I don't really understand how to do it.. The teacher didn't really help me.
 
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  • #2
Start by breaking down each vector into components. Because each of the angles are known, you should be able to break it down in x and y... Make sure to keep the sign straight (West is -x direction, South is -y direction etc...)
 
  • #3
Ok. Thanks.
 
Last edited:
  • #4
Use trig to work out the horizontal and vertical distance moved in each flight between cities.
Then just add them up into a resultant value, remembering to watch out for different directions.
 
  • #5
Got it :) Thanks guys.
 

1. What is a vector?

A vector is a mathematical quantity that represents both magnitude (size) and direction. It is commonly represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow indicating the direction.

2. How do you add vectors?

To add vectors, you must first determine their respective magnitudes and directions. Then, you can use the head-to-tail method or the parallelogram method to add the vectors. In the head-to-tail method, you align the tail of the second vector with the head of the first vector and draw a new vector from the tail of the first vector to the head of the second vector. The resulting vector is the sum of the two original vectors. In the parallelogram method, you draw a parallelogram using the two vectors as adjacent sides. The diagonal of the parallelogram represents the sum of the two vectors.

3. What is the resultant vector?

The resultant vector is the sum of two or more vectors. It represents the combined effect of the individual vectors and is determined by adding the magnitudes and directions of the original vectors.

4. Can you add vectors with different dimensions?

No, vectors can only be added if they have the same dimensions. This means that they must be either both 2-dimensional or both 3-dimensional. If they have different dimensions, they cannot be added together using traditional vector addition methods.

5. What is the importance of adding vectors in science?

Adding vectors is important in science because it allows us to determine the net effect of multiple forces acting on an object. This is useful in fields such as physics and engineering, where understanding the combined effect of various forces is essential in predicting the behavior of objects and systems.

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