# Equations for relative velocity

1. Nov 28, 2012

### UglyNakedGuy

hello everyone,

Can someone kindly show me the equation for relative velocity calculations?

when i search for them via wikipedia, there is only one formula for collinear objects and they move to the same direction...

so what if they move opposite to each?

and what if their motions follow a curvature ...

plz help :P

2. Nov 28, 2012

### pervect

Staff Emeritus
3. Nov 28, 2012

### HallsofIvy

Staff Emeritus
The equation you mention for "relative velocity" is: if object A is moving away from me at velocity u and object B is moving along the same line and in the same direction at speed v (both relative to me) then the speed of object A relative to B is given by
$$\frac{u- v}{1+ \frac{uv}{c^2}}$$

If they are moving in opposite directions, replace "-v" with "+v".

If they are not moving along the same line, draw a line between them and calculate their components of velocity parallel and perpendicular to that line. Apply the formula above to the parallel components only.

4. Nov 28, 2012

### Staff: Mentor

And replace "+v" with "-v". More concisely, reverse the sign of v everywhere in the equation.

5. Nov 28, 2012

### UglyNakedGuy

$$\frac{u- v}{1- \frac{uv}{c^2}}$$