Vectors using the component method

[farhana21]

Use the component method to add the vectors and shown in the figure. The length of is 2.55 m and the angle θ = 31.5°. Express the resultant + in unit-vector notation.

The answer should be in the form of ...i + ...j

so far i have done

3*cos(31.5) = 2.56 so this is for ...i but I am unsure of how to find vector j for the y axis.

Please could someone advise me. All help and guidance given is much appreciated

 

[mfb]

sin? ;)

I don't see a figure.

 

[farhana21]

Please see this thread for figure

https://www.physicsforums.com/showthread.php?t=670846

 

[mfb]

Well, my hint stays the same.
It is just trigonometry.

 

[rezeew]

.

I would like to clarify that the component method is a mathematical technique used to break down a vector into its x and y components, making it easier to add or subtract multiple vectors. It is based on the principles of trigonometry and can be used to solve problems involving vectors in two dimensions.

In this case, the given vector has a length of 2.55 m and an angle of 31.5°. To find the x component, we can use the formula x = magnitude * cos(angle). Therefore, the x component of this vector would be 2.55 * cos(31.5) = 2.17 m.

To find the y component, we can use the formula y = magnitude * sin(angle). Therefore, the y component of this vector would be 2.55 * sin(31.5) = 1.33 m.

Now, we can express the resultant vector + in unit-vector notation by adding the x and y components separately. Therefore, the resultant vector + can be written as 2.17i + 1.33j.

I hope this helps in understanding the concept of the component method and how to use it to add vectors. Keep in mind that the unit vectors i and j represent the x and y directions, respectively. Thank you for considering my response.