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Space, Time and Motion

Resolving and adding vectors

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on splitting a vector into perpendicular components, combining perpendicular vectors for magnitude and direction, scale drawings, and problems on boats, aircraft and a rope at an angle.

What you need to know

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Key term

A force F acts at an angle θ to the horizontal. Give expressions for its horizontal and vertical components.

Numbers

Calculate the horizontal component of a 50 N force acting at 30° above the horizontal.

Numbers

Calculate the vertical component of a 50 N force acting at 30° above the horizontal.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What does it mean to resolve a vector?

    Model answer

    Resolving means replacing the vector by two components at right angles to each other that together have the same effect as the original.

  2. 2

    A force F acts at an angle θ to the horizontal. Give expressions for its horizontal and vertical components.

    Model answer

    The horizontal component is F cos θ and the vertical component is F sin θ.

  3. 3

    Calculate the horizontal component of a 50 N force acting at 30° above the horizontal.

    Model answer

    The horizontal component is 50 cos 30° = 43 N.

  4. 4

    Calculate the vertical component of a 50 N force acting at 30° above the horizontal.

    Model answer

    The vertical component is 50 sin 30° = 25 N.

  5. 5

    Why are the components of a vector normally chosen at right angles to one another?

    Model answer

    Perpendicular components are independent, so each can be dealt with separately without one affecting the other.

  6. 6

    How are two perpendicular vectors added algebraically?

    Model answer

    The magnitude of the resultant is the square root of the sum of their squares, and its direction is given by the arctangent of their ratio.

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