As an example of the usefulness of the first approach, suppose we wish to calculate the distance a cannonball travels when fired with a vertical velocity component v y and a horizontal velocity component ⁠ v x ⁠, assuming it is fired on a flat surface. Assuming no use of directed lengths, the quantities of interest are then R, the distance travelled, with dimension L, ⁠ v x ⁠, ⁠ v y ⁠, both dimensioned as T L, and g the downward acceleration of gravity, with dimension T L.