Two Cartesian reference frames S and S′ have their axes parallel. Frame S′ is obtained from S by a translation of 2m along the positive x-direction and −3m along the y-direction. A particle is at point A with coordinates (1m,4m) measured in frame S at time t1. At a later instant t2 the same particle is observed at point B whose coordinates measured in frame S′ are (6m,−2m).
(i) Write the position vector of the particle at t1 with respect to frame S.
(ii) Express the position vector of point B with respect to frame S.
(iii) Hence obtain the particle’s change in position between the two instants, giving the answer in unit-vector notation.
(iv) Determine the magnitude and the direction (angle with the positive x-axis) of this change in position.