Why are vertical and horizontal motion considered independent?

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Why are vertical and horizontal motion considered independent?

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Answer 1 · 2016-11-02T05:49:42

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

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

For any vector $\to X$ $vecX$ , component in the direction which makes an angle $θ$ $theta$ with the vector is given by $\to X cos θ$ $vecX cos theta$ .
It follows that for $θ = 90^{\circ}$ $theta=90^@$ , (i.e., in the perpendicular direction)
${cos 90}^{\circ} = 0$ $cos90^@=0$
$\Rightarrow \to X {cos 90}^{\circ} = 0$ $=>vecX cos 90^@=0$

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

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Why are vertical and horizontal motion considered independent?

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