If you know the horizontal and vertical components

Scalars & Vectors - OCR A-Level Physics

  • If you know the horizontal and vertical components, you can find the magnitude and direction of the resultant.
  • Use Pythagoras' theoremFor a right-angled triangle: the square of the hypotenuse equals the sum of the squares of the other two sides (c² = a² + b²). for the magnitude.
  • Use trigonometryThe branch of mathematics dealing with the relationships between angles and sides of triangles (sin, cos, tan). (tan) for the direction.
$$F = \sqrt{F_x^2 + F_y^2}$$
$$\theta = \tan^{-1}\left(\frac{F_y}{F_x}\right)$$
  • This only works directly when the two components are at right angles to each other.
  • Always state the direction of the resultant (e.g. '35 degrees above the horizontal' or 'N30E').
Scalars & Vectors Overview
Any single vector can be split into two perpendicular components 5 of 10 Equilibrium