An object of inertia (m_{1}) moving at (v_{1 i}) collides elastically with an object of inertia (m_{2})

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An object of inertia \(m_{1}\) moving at \(v_{1 i}\) collides elastically with an object of inertia \(m_{2}\) initially at rest. Show that the following solution for the final velocities of the two objects after the collision conserves momentum and kinetic energy:

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