7 The particles \(A\) and \(B\) are moving on a smooth horizontal surface directly towards each other. Particle \(A\) has mass 0.4 kg and particle \(B\) has mass 0.2 kg
Particle \(A\) has speed \(4 \mathrm {~ms} ^ { - 1 }\) and particle \(B\) has speed \(2 \mathrm {~ms} ^ { - 1 }\) when they collide, as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{ec39a757-5867-4798-b26c-73cd5746581c-08_392_1064_625_488} The coefficient of restitution between the particles is \(e\)
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1. Find the magnitude of the total momentum of the particles before the collision.
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2. 1. Show that the speed of \(B\) immediately after the collision is \(( 4 e + 2 ) \mathrm { ms } ^ { - 1 }\)
      [0pt] [3 marks]
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3. (ii) Find an expression, in terms of \(e\), for the speed of \(A\) immediately after the collision.
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4. Explain what happens to particle \(A\) when the collision is perfectly elastic.