Orthogonal

Mutually independent; well separated; . So orthogonal is a well understood metaphor, in the jargon of mathematics, philosophy, programming and many other disciplines. Then why not just say "mutually independent" or "well separated"?

Mutually independent is longer than orthogonal, and well separated isn't actually that clear. If it's a common word, and it seems to be, there can't possibly be any harm in using it.

Anyone who is familiar with the normal mathematical meaning of the term should be able to pick up the implications (the two things are measured on different axes), and that includes most of my colleagues. In any case, though, it would seem that the word in this general sense has become common enough in the literature that it's fair game to use. 

 The key concept of orthogonality is that two (or three) things that are orthogonal are independent of the from each other.  For vectors, orthogonal vectors are vectors that are perpendicular to each other.   This wasn't a big deal in one dimensional motion because all vector are parallel or anti parallel, but two dimensional problems are different.

That the example of a car driving horizontally of a cliff.  The car would have a velocity in the x direction (horizontal), but the pull of gravity is straight down, the -y direction.  So that means the acceleration is in the y and the velocity is in the x, they are orthogonal to each other.

What does that mean, well that there will be no change in motion in the x direction (remember acceleration is "how much the velocity of an object changes in one second) but there is a change in the motion in the y direction.

 defination (sort of) by c2.com

 
For simple two dimensional problems the following has to be true


  1. Initial Velocity is entirely in the x Axis
  2. The acceleration is in the y Axis
  3. The acceleration is typically -9.8 m/s/s (free fall)
  4. How far from the edge is the final position in the x direction
  5. The height is the initial position in the y, the final position is normally zero

With all of these vectors how does information in the X relate to information in the Y

So how do you solve two dimensional, well the kinematics problems are filled with vectors, but there is is one scalar in the all of the equation, TIME.  Time is a scalar so it's not vector, and because of that time can move from the y direction to the x direction and vise verses.   So solving time in the x direction solves for it in the y direction. 

The acceleration is typically -9.8 m/s/s (free fall)

How far from the edge is the final position in the x direction

The height is the initial position in the y, the final position is normally zero

For simple two dimensional problems the following has to be true


  1. Initial Velocity is entirely in the x Axis
  2. The acceleration is in the y Axis
  3. The acceleration is typically -9.8 m/s/s (free fall)
  4. How far from the edge is the final position in the x direction
  5. The height is the initial position in the y, the final position is normally zero

Velocity in the x direction

Acceleration in the y direction