We are required to analyze the conservation of kinetic energy in a perfectly inelastic collision.

Kinetic energy:$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}}^{{\mathbf{2}}}}$

Momentum: $\overline{){\mathit{p}}{\mathbf{=}}{\mathit{m}}{\mathit{v}}}$

Using the equations for final velocity in terms of masses and initial velocity for a perfectly inelastic collision, work out the final kinetic energy. Calculate the initial kinetic energy and show that kinetic energy is not conserved. Use variables, no numbers

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