Mario and Luigi are racing their go-karts on Rainbow Road. Both karts, with their occupants, have identical mass M, and travel down Rainbow Road without any friction. Luigi initially moves to the right with speed v0v0. Mario initially moves to the right with speed 3v0v0, so that he collides with Luigi.  Express your answers to the following in terms of M and v0v0.   (a) Determine the total momentum of the system consisting of both go-karts.       (b) Lakitu predicts that the collision will be totally inelastic (that is, that the go-karts stick together). Assuming this is true, determine the speed and direction of motion (left or right) for both go-karts immediately after the collision.       (c) When the collision occurs, Lakitu is surprised to observe that the go-karts separate after the collision, and Luigi subsequently travels to the right with velocity 2.5v0v0. Determine the speed and direction of motion (left or right) for Mario immediately after the collision.       (d) Determine the kinetic energy lost in the actual collision in part (c).​