2. [Maximum mark: 18] An ice-skater is skating such that her position vector when viewed from above at time seconds can be modelled by () = (de"cost (ae" sint with respect to a rectangular coordinate system from a point O, where the non-zero constants a and b can be determined. All distances are in metres. (a) Find the velocity vector at time . [3] (b) Show that the magnitude of the velocity of the ice-skater at time f is given by ae" V ( 1 + 6 -) [4] At time r = 0, the displacement of the ice-skater is given by () and the velocity of the ice-skater is given by () (c) Find the value of a and the value of b [3] 3 (d) Find the magnitude of the velocity of the ice-skater when ? = 2 (2] At a point P. the ice-skater is skating parallel to the y-axis for the first time (e) Find OP [6] AKTUBation Windows