3. (15 pts) A bullet of mass 5 gram horizontally hit a block with mass 500 gram suspended from a light rope. The velocity of the bullet before hitting the block is 500 m/s, and after collision, the bullet stays in the block and moves together with the block. The length of the rope is L = 10 meters, find: 1). After collision, the maximum height the block can reach. 2). Which type of collision is this situation? What is the loss of energy due to the collision? 3). Prove that the maximum height of the block is independent from the length of the rope L.
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