## Moving Particles - Position Vectors and Relative Position Vectors

For any particle moving on a flat surface, we can find the position vector relative to a fixed point, by counting to the right x units, up y units and writing down If instead we move to the left or down then or are negative. Suppose though that the particle starts from the point with velocity After seconds it will have moved by a vector and it' s new position will be at This is illustrated on the graph below. If we have two particles, A and B, both moving Then the position vector of B relative to A is given by If then the position vector of B relative to A is given by and the velocity of B relative to A is . If the velocities of both particles are constant, as in this case then the relative velocity is constant.

If particle A is initially at moving with velocity and B is at at the same time, moving with velocity 9i+10j the the position vector of A at any time is The position vector of B relative to A is and the velocity of B relative to A is  