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3.3. Practice Sets: Vector Addition

Try it!

  1. A resultant displacement with both x and y components negative will be positioned in
    what quadrant?
  2. Suppose a velocity vector is positioned 67° south of east. What is the quadrant for the vector?
  3. a) When adding the x components of all vectors involved in a vector addition question, what do we find?
    b) When adding the y components of all vectors involved in a vector addition question, what do we find?

Practice

  1. A robotic arm is programmed to move in three successive displacements in a factory. The first displacement vector, A, has a magnitude of 2.5 metres and is directed at an angle of 30 degrees north of east. The second displacement vector, B, has a magnitude of 3.0 metres and is directed vertically upward. The third displacement vector, C, has a magnitude of 4.0 metres and is directed at an angle of 50 degrees south of west. Calculate the magnitude and direction of the resultant displacement vector that represents the overall motion of the robotic arm in the factory.
    Answer:

    [latex]1.25 m, 109°[/latex]
  2. A hiker follows the route indicated in the figure below. Find:
    1. The magnitude of the hiker’s displacement.
    2. The direction of the resultant displacement.
    Figure 3.5. Hiking trail vectorial representation

    Answer:

    [latex]8.1 km, 35°[/latex]
  3. Three forces are exerted on a crate placed on a horizontal floor. They are directed as shown in the figure. If the forces have magnitudes F1= 5.00 N, F2= 18.0 N, and F3= 12.0 N, what is the the net force perpendicular to the floor?

    NOTE: The net force is the vector sum of all external forces acting on an object: [latex]\overrightarrow{Fnet}=\sum\overrightarrow{F}[/latex]

     

    Figure 3.6 Forces on a crate vectorial representation

    Answer:

    [latex]9.85 N, 320.3°[/latex]
  4. A group of college students playing a campus scavenger hunt game must follow these directions to reach their destination. First, they must walk 50 metres east to the students’ centre. From the students’ centre they must walk 30 metres north to the science building, then 40 metres at 70 degrees south of west to the cafeteria. Calculate the resultant displacement vector (magnitude and direction) from their starting point to the cafeteria.
    Answer:

    [latex]37.1 m, 348°[/latex]

Challenge Questions

Text Version of the Challenge Question(s)
  • 1. A student drove to her high school, which is located 15 km east from her house. After school, she drove to her soccer practice, which is 10 km south from her high school. Then she drove to a grocery store, located 15 km west from the soccer field. Finally, she drove back to her home. What was the displacement of the student?
    Answer: [latex]0 \text{ km}[/latex]
  • 2. You are hiking at a conservation area and your GPS indicates that your home is 23 km away at a direction of 30° north of west. The only trail that you can use is leading you north for 12 km. After walking that way, how far and in which direction would you have to walk to get home?
    Answer: [latex]19.9 \text{ km}[/latex] with a direction of [latex]181.4^\circ[/latex]

Image Attributions

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College Physics – Fundamentals and Applications Copyright © by Daniela Stanescu, Centennial College is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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