Why are vertical and horizontal motion considered independent?

1 Answer
Nov 2, 2016

We know that in motion problems, displacement, velocity and acceleration all are vector quantities. Only for the sake of simplicity these are written as #s,v and a#.
For sake of completeness these should be written as #vecs, vecv and## veca.#

We also know that for vector quantities, orthogonal component is always equal to zero as shown below.

For any vector #vecX#, component in the direction which makes an angle #theta# with the vector is given by #vecX cos theta#.
It follows that for #theta=90^@#, (i.e., in the perpendicular direction)
#cos90^@=0#
#=>vecX cos 90^@=0#

As such vertical and horizontal components of motion can be treated independently.