A vector quantity has its full effect in a particular direction but it also has reduced effects in other directions.

The effect of a vector in a direction not along its own line of action is called a component of the vector.

The process of finding the magnitudes of the components of a vector is called resolving the vector into its components.

The magnitude of the component of a vector in a direction at 90° to its own line of action is always equal to zero.

This is why it is often useful to resolve a vector into its vertical and horizontal components, these two components can then be considered (almost) as two independent vectors.

The same process can be carried out for any vector quantity.

If an object is thrown vertically upwards, its subsequent motion can be predicted using the equations of motion for bodies moving with uniform acceleration.

If a body is thrown at an angle q to the vertical we can still use the same equations but we must first find the magnitudes of the vertical and horizontal components of the initial velocity of the body.

The vertical component of velocity changes at a uniform rate because of gravity.

The horizontal component of velocity is constant (assuming that air resistance is negligible).

The path followed by the body is a parabola.

use the equations of motion (v = u + at, s = ut + ½at² etc) but the velocities "u" and "v" now refer to the vertical components of the initial and final velocities.

To calculate the range of the projectile, x, we use the equation

where t is the total time in the air and v_h is the horizontal component of the initial velocity.

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© David Hoult 2008