Two point objects both having mass M are placed at positions (0,yM0) and (0,-yM0) in the 2D Cartesian coordinate system and cannot move. A third point object of mass m has initial position (-xm0,0), and moves with initial speed vm0 towards the origin of the system. Assume that no other objects are affecting this system.
(A) Determine the acceleration of the third object as it continues to move.
(B) Find the total potential energy of the system.
(C) Calculate the speed of the third object when it passes the origin of the coordinate system.
(D) Describe possible motion scenarios for the third object after it passes the origin.
(E) Determine the speed vm the moving object must have at the origin that allows it to escape the system.