A particle P is located at A. Another particle Q is located at B 200 m south of A. P starts moving at 2 m/s towards east at some moment and simultaneously Q starts moving at 4 m/s. (i) If Q moved first towards A and on reaching A quickly changed direction and moved towards east, find the time it takes to catch up with P. (ii) If instead Q aimed at a point C east of A at which it arrives at the same time as P, find the elapsed time. (iii) What should be the minimum speed of Q to catch up with P before it moves 50 m from its initial position? (Assume Q catches up by aiming at the position P would reach at the same time as it does)