# RelVel15

If we have the starting location of the different bodies as the relative motions begin then we can determine the line between the two bodies.

We can use this information to great effect if we want to see in subsequent motion if the bodies meet or collide.

Rab means the position of A with respect to B, so if we want to compare this to the Relative Velocity of the particles then

RAB has components in i & j

Lets set up a 1dimensional problem

Ann and Barry are separated by a distance of 100m.

But in terms of Relative position we need to have a direction too.

The Relative positions of Ann with respect to Barry and of Barry WRT Ann are included in the picture above.

These can be found by giving either a location on a coordinate grid and then following the formula for RAB

Then You should find the same result,

So you can probably see that if Barry goes in a negative i direction (and Ann waits patiently) Barry will bump into Ann,

This can be expressed mathematically as

If Barry and Ann are to meet then their Relative Positions will be a multiple of their Relative Velocities

However it might be better if you are going to judge the position of A to B then to move B to A, this will give you a positive value of k.

Work this out and you will see that in order for the two bodies to collide the

value of k will be negative if the bodies are to collide.