5. 5.(a) A cart (#1) on a linear track collides with another cart (#2). Cart #1 has a mass of 2.50 kg and is travelling 5.40 m/s [E]. Cart #2 is initially stationary and has a mass of 7.50 kg. If the collision is perfectly elastic, with no energy losses, what are the final velocities of the two carts? 5.(b) Repeat the above part (a), but where Cart #1 now has double its original mass. 5.(c) Repeat the above part (a), but where Cart #1 now has double its original velocity. 5.(d) Repeat the above part (a), but where Cart #1 has double its original mass, AND, double its original velocity. 5.(e) What mass would Cart #2 have to be for otherwise same circumstances as in part (a), but where the magnitude of Cart #1's final velocity (after the collision), is half of the magnitude of its original 'incoming' (before the collision) velocity? (Is there only one answer or are there 2 or more possible answers?? Explain and show any additional solutions if any.) 5.(f) Repeat the question in part (a) where the two carts get stuck together after the collision. 5.(g) Is it possible for Cart #1 to come to a complete stop after its collision with Cart #2 for some different mass of Cart #2, given everything else is the same as originally describe in part (a)? If so, show how this calculation would work and determine both this other mass for Cart #2 as well as its final velocity. If not, prove with theory and/or examples why not. Use diagrams to help your explanations. 5.(h) If Cart #2 was travelling toward Cart #1 with the same magnitude of velocity as for Cart #1 in part (a), but in the opposite direction, then what will the final velocities be? 5.(i) If Cart #2 is initially (before collision) travelling at 90.0% of the same velocity vector as Cart #1 (same direction, but a little bit slower), then determine the final velocities if everything else is the same as in the original part (a).