# Adding vectors with the component method

• personguything
In summary, the conversation was about finding the resultant of multiple forces and the person had gotten a different answer from the book. They then realized their mistakes in their calculations and were able to correct them. They also mentioned being careful about the quadrant placement for the angle.
personguything
Hi! I know this is pretty basic... I'm teaching myself from a textbook, and I got a different answer from the book...It doesn't have the problem worked out, just the answer. I just need to figure out what mistake I made.

## Homework Statement

Find the resultant of the following forces: (a) 30N at an angle of 40°, with respect to the x-axis, (b) 120N at an angle 135°, (c) 60N at an angle of 260°

The book's answer(and I'm assuming the correct one) is: 85.2N; 148 from +x axis

2. The attempt at a solution
First I name each vector
30N, 40 deg is a | 120N, 135 deg is b | 60N 260 deg is c

Next I find the x and y components for each vector
ax = 30*cos(40) = 23;
ay = 30*sin(40)
---
bx = 120*cos(35) = 98.3;
by = 120*sin(35) = 68.8
---
cx = 60*sin(260) = -59.1;
cy = 60*cos(260) = -10.4
---
Next I find the x and y components of the resultant vector
Rx = ax+bx+cx = 62.2
Ry = ay+by+cy = 62.2

Next I find the hypotenuse(i.e. the magnitude of the resultant vector)
R = √((62.2)^2+(77.7)^2) = 99.5

And finally I calculate the angle of the resultant vector
θ = arctan(77.7/62.2) = 51.3

personguything said:
Hi! I know this is pretty basic... I'm teaching myself from a textbook, and I got a different answer from the book...It doesn't have the problem worked out, just the answer. I just need to figure out what mistake I made.

## Homework Statement

Find the resultant of the following forces: (a) 30N at an angle of 40°, with respect to the x-axis, (b) 120N at an angle 135°, (c) 60N at an angle of 260°

The book's answer(and I'm assuming the correct one) is: 85.2N; 148 from +x axis

2. The attempt at a solution
First I name each vector
30N, 40 deg is a | 120N, 135 deg is b | 60N 260 deg is c

Next I find the x and y components for each vector
ax = 30*cos(40) = 23;
ay = 30*sin(40)
---
bx = 120*cos(35) = 98.3; <---- Isn't the angle 135° ?
by = 120*sin(35) = 68.8
---
cx = 60*sin(260) = -59.1; <---- Looks like you've swapped sin and cos
cy = 60*cos(260) = -10.4
---
Next I find the x and y components of the resultant vector
Rx = ax+bx+cx = 62.2
Ry = ay+by+cy = 62.2

Next I find the hypotenuse(i.e. the magnitude of the resultant vector)
R = √((62.2)^2+(77.7)^2) = 99.5

And finally I calculate the angle of the resultant vector
θ = arctan(77.7/62.2) = 51.3

Redo you calculations after fixing up the bits I've indicated. Be careful about the quadrant placement for the angle.

gneill said:
Redo you calculations after fixing up the bits I've indicated. Be careful about the quadrant placement for the angle.

Thank you! I 100% missed the "35" mistake haha. The cos/sin switch was on purpose, something about it being below the x-axis...Anyway, I worked through it all visually and mathematically and figured it out.

I appreciate it!

Last edited:

## 1. What is the component method for adding vectors?

The component method for adding vectors involves breaking down each vector into its horizontal and vertical components and then adding the corresponding components to find the resultant vector.

## 2. How do I find the horizontal and vertical components of a vector?

To find the horizontal component of a vector, multiply the magnitude of the vector by the cosine of the angle it makes with the horizontal axis. To find the vertical component, multiply the magnitude of the vector by the sine of the angle it makes with the horizontal axis.

## 3. Can I use the component method to add more than two vectors?

Yes, the component method can be used to add any number of vectors. Simply break down each vector into its horizontal and vertical components, add the corresponding components, and then use the Pythagorean theorem to find the magnitude and direction of the resultant vector.

## 4. How do I represent a vector using the component method?

A vector can be represented using the component method by writing its horizontal and vertical components in the form of a column vector. For example, if a vector has a horizontal component of 3 and a vertical component of 4, it can be written as [3, 4].

## 5. What are the advantages of using the component method for adding vectors?

The component method allows for easier visualization and calculation of the resultant vector, especially when dealing with multiple vectors. It also allows for the use of trigonometric functions to calculate the components, which can be more precise than using graphical methods.

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