# The independance of horizontal and vertical motion...

 P: 236 Obviously it is possible to prove the independance of horizontal and vertical motion empirically - we only need look at projectile motion following a parabolic path. However, I have never found a convincing algebraic proof the for the independence of these 2 types of motion. I have asked my physics teacher and he says that it can apparetly be proved by treating Gravity as a Vector, and then assessing the overall motion of a body - apparently things like "gcos90" appears, which obviously equal "0", and this can be used to show the independance of horizontal and vertical motion. If anyone could supply me with a convincing algebriac proof i would be really greatful! Thanks in advance.
Emeritus
 Emeritus Sci Advisor P: 7,631 The independance of horizontal and vertical motion... You also need to define how vectors multiply before you can say that$$\hat{x}$$ and $$\hat{y}$$ are orthagonal. A metric such as ds^2 = dx^2 + dy^2 is one way of giving the necessary defintion of the vector product $$\hat{x} \cdot \hat{y}$$, and a diagonal metric such as the specific example above is necessary and sufficient to make these two vectors orthagonal.