A swimmer starts at pier P on a calm lake. She swims 200m due east to buoy Q and then 150m due south to buoy R. A rescue boat is anchored at point B, which lies 100m due west of buoy R.
(i) Calculate the magnitude of the swimmer’s resultant displacement from pier P to buoy R.
(ii) Determine the position of the rescue boat B relative to the pier P, expressing your answer as signed east and south components.
(iii) If the rescue boat B is taken as the new reference point and east is kept as the positive x-direction while north is the positive y-direction, find the position vectors (components with units and proper signs) of pier P and buoy Q relative to B.