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Verify your answer to part (b) by calculating the initial and final kinetic energies of the system in joules.

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Final answer:

Using the provided information, the initial kinetic energy was calculated to be 225 J and the final kinetic energy as 64 J, with a difference of -161 J, indicating a loss of kinetic energy, consistent with the principle of conservation of momentum in a system.

Step-by-step explanation:

The student's question pertains to the calculation of kinetic energies before and after a collision in a Physics context. As per the reference information, we need to verify the final and initial kinetic energy values given a specific scenario.

The initial kinetic energy (KEi) is calculated using the equation KEi = 0.5 * m * v2, where m is the mass and v is the velocity. Substituting the given values, KEi is (0.5)(2.0 kg)(15 m/s)2 = 225 J. For the final kinetic energy (KEf), the combined mass's velocity after the collision is used, resulting in KEf = (0.5)(7.0 kg)(4.286 m/s)2 = 64 J. Therefore, the difference in kinetic energy due to the collision is 225 J - 64 J = -161 J, indicating kinetic energy has been lost, likely converted into other forms such as heat or sound due to non-conservative forces during the collision.

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