3.3. Practice Sets: Vector Addition

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3.3. Practice Sets: Vector Addition

Try it!

A resultant displacement with both x and y components negative will be positioned in
what quadrant?
Suppose a velocity vector is positioned 67° south of east. What is the quadrant for the vector?
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. 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]