Vector operations in two dimensions

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Intros
Lessons
  1. Introduction to vector operations in two dimensions
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Examples
Lessons
  1. Perform tip-to-tail addition in two dimensions

    A student arrives at school and from the entrance walks 20 m north to go to English. After, they walk 30 m east to physics class. What is their overall displacement? Answer with a vector diagram and a vector equation that describes the displacements.

    1. Solve vector additions graphically

      Solve the following vector equations graphically:

      i. Δd1+Δd2=Δdres\Delta \vec{d}_{1} + \Delta \vec{d}_{2} = \Delta \vec{d}_{res}

      PHYS 1 3 2a

      ii. v1+v2=vres\vec{v}_{1} + \vec{v}_{2} = \vec{v}_{res}

      PHYS 1 3 2b

      iii. A+B+C=D\vec{A} + \vec{B} + \vec{C} = \vec{D}

      PHYS 1 3 2c
      1. Solve vector subtraction, multiplication, and division graphically

        Solve the following vector equations graphically:

        i. Δd1Δd2=Δdres\Delta \vec{d}_{1} - \Delta \vec{d}_{2} = \Delta \vec{d}_{res}

        PHYS 1 3 3b

        ii. 2v1+0.2v2=vres2\vec{v}_{1} + 0.2 \vec{v}_{2} = \vec{v}_{res}

        PHYS 1 3 3c

        iii. A2BC2=D\vec{A} - 2\vec{B} - \frac{\vec{C}}{2} = \vec{D}

        PHYS 1 3 3c
        1. Write and draw the angles of vectors relative to compass directions PHYS 1 3 4

          i. Write the vector using vector notation

          ii. Draw the vector C\vec{C} = 2.5 m [40° S of E] on a set of compass axes.

          1. Calculate two dimensional displacement with Trigonometry

            A car drives at 13.8 m/s [W] for 115 s. It then turns left and travels south at 19.4 m/s for 135 s. Find the displacement of the car from its starting position.