Horizontal motion and vertical motion are effectively independant

[Cheman]

Is there a way to mathematically or physically prove that horizontal motion and vertical motion are effectively independant? ie - is it possible to derive this fact from, say, vectors?

I know that is is true - the parabola shape of projectiles wouldn't make sense otherwise, but is there a convincing proof for it? It would just allow me to accept this fact if i had a proof, and then i would be happy to use the procedure!

Thanks in advance.

 

[kirovman]

When you drop something from a building, does it move eratically all over the place, or does it fall down in a straight line? (assuming nil air resistance)

I think the fact they are independent is just postulate.

To get the proof, do some experimentation.

Everything is only theory until you get down to the lab to check it out.

 

[Cheman]

But surely it can be prooved mathematically?

 

[Nenad]

it can be prooven mathematically by the analysis of experiments. It seems simple to understand, the vector is bromen up into two compnenets one vertical and the other horizontal. To understand why this happens is like asking why is there inertia. Why do bodies with mass oppose acceleration. Nobody knows, but it's just common sence.

 

[PBRMEASAP]

Is there a way to mathematically or physically prove that horizontal motion and vertical motion are effectively independant? ie - is it possible to derive this fact from, say, vectors?

Yes. The motion is determined by Newton II, F = ma, which is a vector equation. Since the two vectors are equal, their individual components must be equal. The x and y components of a vector are completely independent of each other, since the x direction is 90 degrees to the y direction.

 

[BigStelly]

force is what causes change in velocity, assuming no air resitance... a projectile changes velocity in the vertical direction during its flight... due to gravity. The horizontal however is constant... that proves it right there more or less. The horizontal remains the same regardless of the motion in the vertical direction due to gravity... need more than that?