Problem 3. Colliding boxes. The next two problems deal with colliding boxes. A box of mass m slides to the right with speed vm on a frictionless horizontal surface. It collides with a second box of mass 3m that is initially at rest. Before Collision: vm PRIORITY 3m m (a) Suppose the box of mass m sticks to the box of mass 3m. After Collision: ORITY m PRIORITY 3m What is the ratio Ki/Kf of the initial to the final kinetic energies of the system of two boxes i.e., the ratio of the kinetic energy before the collision to the kinetic energy after the collision? If the ratio is not 1, where did the energy go? Discuss your strategy briefly before solving this problem. (b) Now suppose that instead of the boxes sticking together, the collision is completely elastic. What is the velocity of the box of mass m after the collision? Discuss your strategy briefly before solving this problem.