Addition of Vectors by means of Components

In summary: Since the x- and y-components of C are given in the problem, you can use the Pythagorean theorem to find the length of the hypotenuse and the trigonometric functions to find the missing angle.
  • #1
RKNY
13
0

Homework Statement


A football player runs the pattern given in the drawing by the three displacement vectors A, B, and C. The magnitudes of these vectors are A = 5 m, B = 14.0 m, and C = 23.0 m. Using the component method, find the magnitude and direction of the resultant vector A + B + C
http://www.webassign.net/CJ/cj6_1-55.gif" .


Homework Equations


Rx = Ax + Bx + Cx
Ry = Ay + By + Cy



The Attempt at a Solution


Components of A
Ax = 0
Ay = 5

Components of B
Bx = 14.0
By = 0

Components of C
Cx = 18.8
Cy = -23.0

Rx = 32.8
Ry = -18.2

Took the square root of Rx^2 + Ry^2 and found it out to be the answer of 37.5.

I put it in but it tells me that it isn't right?
 
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  • #2
Check your y component of vector C.
 
  • #3
cristo said:
Check your y component of vector C.

It worked out okay, thanks a bunch!
 
  • #4
I have that exact problem now, and I can't come up with the correct answer
 
  • #5
Welcome to PF!

pstfleur said:
I have that exact problem now, and I can't come up with the correct answer

Hi pstfleur! Welcome to PF! :smile:

Show us what you've done, and where you're stuck, and then we'll be able to help! :wink:
 
  • #6
Nevermind..Figured it out!
 
  • #7
Thanks a lot thou, I will be sure to use this site through out the semester :)!
 
  • #8
Can somebody please tell me how to figure out Cx and Cy. I'm completely lost on how to get those values.
 
  • #9
Make a right triangle with C being the hypotenuse. Use the 35-degree angle in your construction.
 

Related to Addition of Vectors by means of Components

1. What is the concept behind addition of vectors by means of components?

The concept behind adding vectors by means of components is to break down each vector into its horizontal and vertical components, and then add these components separately. This method is particularly useful when dealing with vectors in two dimensions.

2. How do you find the components of a vector?

To find the components of a vector, you can use trigonometric functions such as sine and cosine. The horizontal component is found by multiplying the magnitude of the vector by the cosine of the angle it makes with the x-axis. Similarly, the vertical component is found by multiplying the magnitude of the vector by the sine of the angle it makes with the y-axis.

3. What are the steps for adding vectors by means of components?

The steps for adding vectors by means of components are as follows:
1. Break down each vector into its horizontal and vertical components.
2. Add the horizontal components together and the vertical components together separately.
3. Use the Pythagorean theorem to find the magnitude of the resultant vector by taking the square root of the sum of the squares of the horizontal and vertical components.
4. Use trigonometric functions to find the direction of the resultant vector by taking the inverse tangent of the vertical component divided by the horizontal component.

4. What are some real-world applications of addition of vectors by means of components?

Addition of vectors by means of components is used in various fields such as engineering, physics, and navigation. For example, in engineering, this concept is used to determine the forces acting on a structure, while in physics it is used to calculate the net force on an object. In navigation, addition of vectors by means of components is used to calculate the velocity and direction of moving objects.

5. What is the difference between adding vectors by means of components and graphically?

The main difference between adding vectors by means of components and graphically is that the former involves breaking down vectors into their horizontal and vertical components, while the latter involves drawing the vectors on a coordinate system and using the parallelogram method to find the resultant vector. Generally, adding vectors by means of components is more accurate, while adding vectors graphically is a more visual representation of vector addition.

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