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Vector components

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Intros
Lessons
  1. Introduction to vector components:
    • What are x and y components?
    • How to break a vector into its components
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Examples
Lessons
  1. Break a displacement into vector components

    A boat sails 33.0 km at 55.0° north of west. What are the north and west components of its displacement?

    1. Use components of velocity for calculations

      A plane that is taking off travels at 67.0 m/s at a 15.0° angle above the horizontal.

      1. How long does it take the plane to reach its cruising altitude of 12.0 km?
      2. If the plane is headed east, how far east has it travelled in this time?
      1. Add two 2D vectors using components

        Solve the equation v⃗1+v⃗2=v⃗res\vec{v}_{1} + \vec{v}_{2} = \vec{v}_{res} by breaking v⃗1\vec{v}_{1} and v⃗2\vec{v}_{2} into their x and y components.

        PHYS 1 4 3
        Topic Notes
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        In this lesson, we will learn:

        • What are x and y components?
        • How to break a vector into its components
        • Problem solving with vector components

        Notes:

        • Components of a vector are other vectors that add up tip-to-tail give you the original vector.
          • The x and y components of a vector are the components that are pointed directly in the x and y directions, respectively, and are useful for solving problems.
          • The x and y components can be found with trigonometry, since they always form a right triangle with the original vector.
        Right Triangle Trigonometric Equations

        sin⁡(θ)=opp.hyp.\sin(\theta) = \frac{opp.}{hyp.}

        cos⁡(θ)=adj.hyp.\cos(\theta) = \frac{adj.}{hyp.}

        tan⁡(θ)=opp.adj.\tan(\theta) = \frac{opp.}{adj.}

        a2+b2=c2a^{2}+b^{2}=c^{2} (Pythagorean theorem)

        θ\theta: angle, in degrees (°)

        opp.opp.: side opposite angle

        adj.adj.: side adjacent angle

        hyp.hyp.: hypotenuse of triangle (longest side, side opposite 90° angle)

        aa and bb: non-hypotenuse sides of triangle

        cc: hypotenuse of triangle