Mechanics

Resolving a Vector into two Perpendicular Components

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.

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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