Section 3-Algebraic Vector Addition-Part 2

The second part of algebraic vector addition is to add our components and determine our resultant vector (the fancy way of saying our final answer).

If you want to add two or more vectors together using the algebraic method, you first need to decompose each vector into its x and y components. Be sure to label them so you know which components belong to which vector, for example as shown in the below diagram.

Ensure you've given the correct positive and negative signs to the components depending on the direction they point. After you've arrived at the total x and y values you can use the Pythagorean theorem to determine the magnitude of the resultant vector, and the tangent function to find the angle, as shown in the diagram I prepared below.

If you'd like some extra information on summing vectors algebraically, check out the website: https://www.physicsclassroom.com/class/vectors/Lesson-1/Component-Addition

Practice Problems

Complete the following practice problems using the algebraic method of vector addition, rounding your answers to the nearest tenth. It would be best to attempt these problems before our Zoom meeting for this section that way if you have any questions you can ask them during our meeting.

1. 5 N @ 25° North of West + 3 N @ 5° West of North
   • Answer: 7.9 N @ 72.5° West of North
2. 2 N @ 30° East of North + 2 N @ 45° South of West
   • Answer: 0.5 N @ 52.5 West of North

Assignment 3 – Due (Date filled in for actual course to meet the course timeline.)

Your assignment is to answer the following questions on paper, showing all your work. Be sure to sketch each vector, break each vector into components, add the components, and then determine the resultant vector when summed. Please use up (North) as your positive y direction and right (East) as your positive x direction, rounding your answers to the nearest tenth (the first decimal place).

1. 5 N @ 65° North of East + 2 N @ 15° South of East
2. 3 m @ 45° South of East + 1 m North
3. 4 N @ 85° North of West + 2 N @ 5° North of East

When your assignment is complete, scan each page in your assignment or take a clear, high-resolution picture of each page, and then submit the images to me via email. Be sure to number each of your pages in the corner so I know what order your scanned pages go in.

Once you’ve completed all the tasks and learning for this section, please select an option on the Poll.ly form below to let me know how you’re feeling about your understanding of this section. You can cast your vote by clicking the icon beside the answer you want to pick.