Vector addition by components
Adding vectors using components
We can use the fact that vectors can be resolved into components to enable us to add vectors using basic trigonometry. Consider the following example.
Albert walks 7m N 44.6o E then 4 m E 42.2o S. What is his displacement relative to his starting position? Use the navigation bar at the bottom of the image to click through the steps for solving this problem - see text below this image for description of steps.
Worked example:
- you should always make a scale drawing of vector problems as you work
- Draw the first vector, u
- Draw the second vector, v, head to toe
- Draw the resultant vector, r
- Resolve u into 2 right angle vectors, uy and
- ux
- Calculate ,
- Resolve v into 2 perpendicular vectors, vy and
- vx
- Calculate ,
- Calculate
- Calculate
- Calculate
- Calculate
Try it yourself
Rewind the frames back to the step 3. Move the blue points to create new problems. Calculate each step then advance the frame to check your answer.