Show that in an elastic collision between two objects of inertias (m_{1}) and (m_{2}), with initial (x)

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Show that in an elastic collision between two objects of inertias \(m_{1}\) and \(m_{2}\), with initial \(x\) components of velocity \(v_{1 \mathrm{i}}>0\) and \(v_{2 \mathrm{i}}=0\), the final \(x\) components of velocity are

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Discuss the cases \(m_{1} \ll m_{2}, m_{1}=m_{2}\), and \(m_{1} \gg m_{2}\). Using everyday objects, give an example of each of these three cases. 

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