8 Two spheres \(A\) and \(B\) are free to move on a smooth horizontal surface. The masses of \(A\) and \(B\) are 2 kg and 3 kg respectively.
Both \(A\) and \(B\) are initially at rest.
Sphere \(A\) is set in motion directly towards sphere \(B\) with speed \(4 \mathrm {~ms} ^ { - 1 }\) and subsequently collides with sphere \(B\) The coefficient of restitution between the spheres is \(e\)
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1. 1. Show that the speed of \(B\) immediately after the collision is $$\frac { 8 ( 1 + e ) } { 5 }$$ 8
2. (ii) Find an expression, in terms of \(e\), for the velocity of \(A\) immediately after the collision.
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3. It is given that the spheres both move in the same direction after the collision. Find the range of possible values of \(e\)
   [0pt] [2 marks]
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4. 1. The impulse of sphere \(A\) on sphere \(B\) is \(I\)
      The impulse of sphere \(B\) on sphere \(A\) is \(J\)
      Given that the collision is perfectly inelastic, find the value of \(I + J\)
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5. (ii) State, giving a reason for your answer, whether the value found in part (c)(i) would change if the collision was not perfectly inelastic.
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