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This lecture covers the analysis of elastic and inelastic collisions, discussing the conservation of kinetic energy and momentum. Examples include collisions between clay balls, falling buttered toast, and nuclear fusion. The concept of perfectly inelastic collisions is explained, where kinetic energy is converted into heat. The lecture also delves into 2D elastic collisions, emphasizing the conservation of momentum and kinetic energy. Special cases like equal mass collisions and collisions on air tables are explored, highlighting the complexities of real-world collisions. The analysis extends to scenarios like rocket propulsion, where varying mass introduces additional considerations in momentum conservation.