3 vectors using south, northeast, and west

[chocolatelover]

[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

 

[Kurdt]

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.

 

[chocolatelover]

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

 

[Kurdt]

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.

 

[chocolatelover]

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

 

[Kurdt]

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

 

[chocolatelover]

Thank you very much

Regards