A cube of mass m = 0.2 Kg is placed on a horizontal plane, and is in contact with the extremity of a spring of elastic constant k = 100 N/m, compressed by 20 cm with respect to its equilibrium position. The cube is initially at rest. When the spring is left free, the cube is thrown along the path shown in the figure where it crosses an area AB of the plane of length s = 1 m and dynamic friction coefficient ud = 0.005. Then it goes up a smoothed (no friction) inclined plane BC of length 1 = 0.5 m which forms an angle O=30° with the horizontal plane. Determine:

(a) The speed of the cube at the beginning (A) of the unsmoothed region of the surface and the speed at the end (B) of it (4 points) (b) The modulus of the speed of the cube at the end of the inclined plane (C) (4 points) (c) The law of the motion of the object after it left the point C (4 points).