1. Two particles, A and B, of the same mass :11, moving on the x-y plane, have positions at time I described by the following vectors (a), R are positive constants): n. 710') : R(cos(a)r)f +sin(wr);) 173(2') : Rf+ 2R(cos (or? +sin (orj) (a) Sketch the trajectory of the particles and describe their motion. [7 marks] (b) The particles then collide head-on. When and where does it happen? [3 marks] (0) Find the velocities of the particles immediately after collision if the collision is (i) completely inelastic, and (ii) elastic. [11 marks]