1. 1. On a large flat frictionless surface, a 3.00 kg mass travelling at 5.00 m/s collides with a 4.00 kg mass travelling at 2.25 m/s. After the collision, the 3.00 kg mass is now travelling at only 1.75 m/s. 1.(a) What magnitude of velocity must the 4.00 kg mass be travelling at if there was no energy lost in the collision? 1.(b) Repeat the question in part (a) above, but where this time there was a loss of a total of 9.57 Joules from the collision itself (in the form of some light damage to the masses and sound and thermal energy losses). What is the revised final magnitude of velocity must the 4.00 kg mass if the final velocity of the 3.00 kg mass was only 1.25 m/s this time? 1.(c) After the energy-losing collision in (b), the 3.00 kg mass continues onward in a straight line and hits a horizontally placed spring attached to a fixed support block, bolted down to the flat surface the masses are moving across. It compresses the spring up to a maximum point of 3.48 cm before the spring just starts to move back and now push the mass away. What must the spring constant of this spring be? Assume in this part, part (c), that there are no energy losses from the mass interacting with this spring. 1.(d) Assume now that there is a 12.5% energy loss from the 3.00 kg mass's entire overall collision with the spring described in (c). In this case what will be the final velocity vector for this mass after it leaves the spring completely heading back out (i.e. after the spring has expanded back against this mass and pushed it away)? Assume the incoming velocity of the 3.00 kg mass had a vector direction of [E24.2'N]