Calculating Vector Magnitudes by Breaking Down Components

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Discussion Overview

The discussion revolves around the process of adding vector magnitudes by breaking them down into their components. Participants explore the methodology for calculating resultant vectors, including the importance of direction and the use of trigonometric functions to resolve vectors into their x and y components.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant asks how to add two vector magnitudes and find their x components.
  • Another participant suggests that the easiest way to add vectors is by component and emphasizes that simply adding magnitudes does not yield meaningful results.
  • A participant provides specific vector values (V1=3.0 m/s along the +x-axis and V2=2.0 m/s) but expresses uncertainty about the addition process.
  • Another participant highlights the necessity of specifying both magnitude and direction for each vector when performing vector addition.
  • A later reply outlines a method for breaking down vectors into their x and y components using trigonometric functions, explaining how to add these components and apply the Pythagorean theorem to find the resultant magnitude.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the addition of vectors, as there is uncertainty regarding the direction of V2 and the overall process of vector addition. Multiple viewpoints on the methodology are presented.

Contextual Notes

Some assumptions about the directions of vectors are not explicitly stated, and there are unresolved questions about how to handle vector addition without complete information on all components.

SMS
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How do you add two vector magnitudes and find x components?
 
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The easiest way to add vectors is by component. You then find the magnitude of the resultant. You cannot simply add magnitudes and get a meaningful result.
 
??

OK, V1= of 3.0 m/s and is directed along the +x-axis. V2=2.0 m/s. So V3 = V1+V2. Right.


I was never really shown how to add vectors.


Thanks.
 
SMS said:
OK, V1= of 3.0 m/s and is directed along the +x-axis.

See how you posted a magnitude and a direction there?

You need to do that every time.

V2=2.0 m/s.

In what direction?
 
to add vectors you have to break them down to their x and y components. ie let's say a vector has a magnitude of 'A' and an angle of 'K', you have to get the magnitude in the x and the magnitude in the y, so Ax=A cos (K) and Ay=A sin (K), now that you broke it down to Ax and Ay you can add it to other vector that you have broken down, just add the like parts like Bx+Ax and By+Ay the use the pathagorean theom to get the resultent magnitude (x^2+y^2=z^2) where z is the resultant magnitude.
 

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