How to Find the X Component of a Vector | Decomposing Vectors Homework

  • Thread starter Mr Davis 97
  • Start date
  • Tags
    Vectors
In summary, when finding the x component of a vector that is pointing in a direction specified in degrees, there are two ways to do it. One way is to tack on a negative sign and calculate -(magnitude)cos(angle). The other way is to not tack on a negative sign and calculate (magnitude)cos(180-angle). Either method is acceptable, as long as you are aware of the direction and use the appropriate angle in the cosine function.
  • #1
Mr Davis 97
1,462
44

Homework Statement


The magnitude of the vector is 6 m, and points 35 degrees north of west. Find the x component of the vector.

Homework Equations



x = |R|cos(theta)

The Attempt at a Solution



I am confused about what degrees to input into the cosine function. I know that the vector is pointing 35 degrees north of west, which means that the x component will be negative, but there are two ways I could do it am I am not sure which one I should do. First, I could tack on a negative and calculate -(6 m)cos35 = -4.9 m. Another way is not tack on a negative and calculate (6 m)cos145 = -4.9 m. Which method is better, and which one should I use on a regular basis?
 
Physics news on Phys.org
  • #2
Both ways are fine, as long as you don't try to memorize a rule and blindly apply it. Personally, I like the first approach, and just tack on the negative sign when I know there should be one.
 
  • #3
Mr Davis 97 said:

Homework Statement


The magnitude of the vector is 6 m, and points 35 degrees north of west. Find the x component of the vector.

Homework Equations



x = |R|cos(theta)

The Attempt at a Solution



I am confused about what degrees to input into the cosine function. I know that the vector is pointing 35 degrees north of west, which means that the x component will be negative, but there are two ways I could do it am I am not sure which one I should do. First, I could tack on a negative and calculate -(6 m)cos35 = -4.9 m. Another way is not tack on a negative and calculate (6 m)cos145 = -4.9 m. Which method is better, and which one should I use on a regular basis?
Well, you could learn the angles for the cardinal points of the compass, but why do that when you can just make something up?

East = 0°
North = 90°
West = 180°
South = 270°
 
  • #4
SteamKing said:
Well, you could learn the angles for the cardinal points of the compass, but why do that when you can just make something up?

East = 0°
North = 90°
West = 180°
South = 270°

Huh?
 
  • #5
Mr Davis 97 said:
Huh?
You've never seen the following diagram (or a similar one)?:
ucad.gif
It should have been used when you studied trigonometry.

After all,
cos (0°) = 1.0
sin (0°) = 0.0

cos (90°) = 0.0
sin (90°) = 1.0

cos (180°) = -1.0
sin (180°) = 0.0

cos (270°) = 0.0
sin (270°)= -1.0

etc., etc.
 

1. What is the X component of a vector?

The X component of a vector is the horizontal length or magnitude of the vector. It is the projection of the vector onto the X-axis.

2. How do you find the X component of a vector?

To find the X component of a vector, you can use the formula X = |V| * cos(θ), where |V| is the magnitude of the vector and θ is the angle between the vector and the X-axis.

3. Can you decompose a vector into its X and Y components?

Yes, a vector can be decomposed into its X and Y components using trigonometry. The X component is the horizontal projection of the vector and the Y component is the vertical projection.

4. Why is it important to find the X component of a vector?

Finding the X component of a vector is important in many applications, such as physics and engineering. It allows us to analyze the motion of an object in a specific direction and calculate the forces acting on it.

5. What is the difference between the X component and the Y component of a vector?

The X component of a vector is the horizontal projection of the vector, while the Y component is the vertical projection. They are perpendicular to each other and together make up the magnitude and direction of the vector.

Similar threads

Knowing when to decompose weight vector vs. normal vector
    • Introductory Physics Homework Help
Replies
6
Views
1K
Doubt about the 2nd position vector direction in a particle's movement
    • Introductory Physics Homework Help
Replies
4
Views
690
Syntax Error? x and y components of E field in unit vector form
    • Introductory Physics Homework Help
Replies
13
Views
601
Finding the x component of position vector
    • Introductory Physics Homework Help
Replies
3
Views
168
Finding z component of a unit vector
    • Introductory Physics Homework Help
Replies
2
Views
2K
Am I Calculating the Components of V3 Correctly?
    • Introductory Physics Homework Help
Replies
9
Views
2K
Finding velocity for projectile given distances and launch angle
    • Introductory Physics Homework Help
Replies
3
Views
1K
Overall displacement vector from a walking trip....
    • Introductory Physics Homework Help
Replies
19
Views
7K
To find the closest approach of two ships
    • Introductory Physics Homework Help
Replies
2
Views
1K
Confusion with force components
    • Introductory Physics Homework Help
Replies
21
Views
2K

Hot Threads

Recent Insights

Back
Top