2. A particle has the position function given by r(t) = (cost?,sint?,1),t > 0. (a) [2p] (i) Sketch the trajectory of the particle. Indicate the direction the particle is moving. (ii) Find the velocity and the speed of the particle as functions of . (iii) Find the acceleration and the tangential and normal components of the acceleration as functions of . (b) [2p] Suppose that a target is placed at the point at P(2,0,1). (i) At what point on the circle should the particle be released to hit the target? (ii) At what time should the release take place? Use the smallest value of that will work. (iii) How long will it take the particle to hit the target