In Fig. I, a quarter of a cylindrical pipe of radius 2 m is xed to a vertical wall. A rod AB is placed next to the wall. The rod touches the wall at A, the pipe at P and the oor at B at the same time. Let AABO = (9. (a) Show that AB = (2 tan 0+ 2 cot 0) m. (b) Show that the minimum possible length of the rod is 4 m. (c) Suppose the length of the rod is 5 m. Now the rod slides down so that the end B of the rod moves towards C, as shown in Fig. 11. The rod touches the pipe and the oor at the same time while sliding. Let x m be the horizontal distance from the end A of the rod to the wall and y m be the vertical distance from the end A of the rod to the oor. . . 1 . . (I) When 6' = E , the rate of change of 615 rad/s. F1nd the rate of change of x at thls moment. 6 5 (ii) Is it possible that the horizontal speed that A is moving to the right is % times the vertical speed that A is moving downward? Explain your