3 vectors using south, northeast, and west

  • Thread starter chocolatelover
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In summary, the problem involves a particle undergoing consecutive displacements of 3.80 m south, 8.40 m northeast, and 14.0 m west. The resultant displacement is found by using vector addition to get a magnitude of 22.2 and a direction of 45°. The northeast vector has i and j components, while the south and west vectors have negative i and j components.
  • #1
chocolatelover
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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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  • #2
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.
 
  • #3
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:
  • #4
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.
 
  • #5
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
 
  • #6
South and west are negative, so for the i's it would be 5.9 + (-14.0) etc.
 
  • #7
Thank you very much

Regards
 

Related to 3 vectors using south, northeast, and west

1. What are 3 vectors using south, northeast, and west?

Three vectors using south, northeast, and west are commonly known as displacement vectors. They represent the direction and magnitude of an object's movement in a 2-dimensional space.

2. How do you calculate the magnitude of a vector in the south direction?

The magnitude of a vector in the south direction can be calculated using the Pythagorean theorem. First, determine the length of the vector in the south direction. Then, square this value and add it to the square of the length in the west direction. Finally, take the square root of this sum to find the magnitude of the vector.

3. Can a vector have multiple components, such as south and west?

Yes, a vector can have multiple components, including south and west. In fact, any vector in a 2-dimensional space can be broken down into its horizontal and vertical components, making it easier to calculate its magnitude and direction.

4. How can you represent a vector using northeast direction?

A vector in the northeast direction can be represented using both its magnitude and direction. Its magnitude can be represented by the length of the vector, while its direction can be represented by the angle formed between the vector and the horizontal axis.

5. What is the difference between a vector and a scalar?

A vector is a quantity that has both magnitude and direction, while a scalar is a quantity that only has magnitude. Vectors can be represented by arrows, while scalars are represented by numerical values. Examples of vectors include displacement, velocity, and force, while examples of scalars include distance, speed, and mass.

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