3 vectors using south, northeast, and west

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The discussion revolves around calculating the resultant displacement of a particle undergoing three consecutive displacements: 3.80 m south, 8.40 m northeast, and 14.0 m west. Participants clarify that the south and west displacements should be represented as negative components in a 2D coordinate system, while the northeast vector has equal i and j components due to its 45-degree angle. After computing the components, one participant arrives at a magnitude of 22.2 for the resultant displacement and confirms the direction as 45 degrees. The importance of using vector addition and proper notation for direction is emphasized throughout the conversation. Accurate representation of vector components is crucial for solving such displacement problems effectively.
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[SOLVED] 3 vectors using south, northeast, and west

Homework Statement


A particle undergoes the following consecutive displacements: 3.80 m south, 8.40 m northeast, and 14.0 m west. What is the resultant displacement?


Homework Equations





The Attempt at a Solution



This means that I have 3.80j, 8.4i, and 14.0k, right? I could then add up all of the x components and y components, right? or do I need to use the law of cos?

thank you very much
 
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No. This is a 2D problem. Conventionally you would have -3.8j for south and -14.0i for west. North East will be a vector of components of i and j. Try drawing a diagram to help you.
 
Thank you very much

I drew a diagram, but the triangle does not seem to be a perfect right triangle. Wouldn't I also have 8.4k? Could you tell me what formula I would need to solve this problem? or would I need to draw it out on graph paper and measure the angles?

Vector A would be (0i+3.8j),vector B would be 8.4k , and vector C would be (14.03i+oj), right? or is the 8.4 part extra information that it is not needed?

I added up the components and got:

Vector A+B=14.03i+3.8j

R=square root of (14.03)^2+(3.8)^2=14.5

Does that look correct? How would I go about solving for the angle?

Thank you
 
Last edited:
The northeast vector will have i and j components. Northeast indicates the vector is 45 degrees north of east, so the components will be equal.

The other two vectors will have negative components in standard notation since i is taken to be the direction east and j is taken to be in the north direction.

Then one will use vector addition to find the resultant displacement.
 
Thank you very much

I found the x and y components of the northeast vector to be 5.9. I then added up the i's and j's and got 19.93 for the i's and 9.7 for the j's.

Magnitude=square root (19.93)^2+(9.7)^2=22.2

direction=45°

Does that look right?

Thank you very much
 
South and west are negative, so for the i's it would be 5.9 + (-14.0) etc.
 
Thank you very much

Regards
 

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