I don't really get the relative velocity formula...
V(a rel b) = V(a rel C) – V(b rel c)
Hey! What the formula actually does mechanically is a little tricky to explain. Essentially, it lets you measure the relative velocity between two frames of references. Best done with an example I think.
Say that you're sitting down, watching two people run past you in the same direction. You measure the first runner as 9 kilometres an hour, and the second at 7 kilometres an hour. For the formula, that's \(v_{ac}\) and \(v_{bc}\); the two velocities relative to a third reference frame - You! So in the formula, C represents the frame of reference of the measurer, and A and B represents two moving bodies.
The formula lets you calculate the velocity of A
relative to B, meaning, the second runner is watching the first runner. How fast does he measure? The answer is, \(v_{ab}=v_{ac}-v_{bc}=9-7=2\) kilometres an hour. This makes sense, the first runner is moving 2 kilometres faster than the second runner, so from the frame of reference of the second runner, they'd say the first runner is moving away at 2 kilometres per hour.
The trick here is the frames of reference, and recognising that we don't always have to measure velocities with respect to the ground. We can measure them with respect to any inertial frame of reference. In this case, we choose the second runner; the first runner is moving 2 kilometres faster than that, so the relative velocity is 2 kilometres an hour.
The formula should only be used once you've got an intuitive understanding of how it works, otherwise it leads to trouble
I hope this helps!!