CAIE FP2 2011 June — Question 4

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2011
SessionJune
TopicMomentum and Collisions 2

4 Two uniform spheres \(A\) and \(B\), of equal radius, are at rest on a smooth horizontal table. Sphere \(A\) has mass \(3 m\) and sphere \(B\) has mass \(m\). Sphere \(A\) is projected directly towards \(B\), with speed \(u\). The coefficient of restitution between the spheres is 0.6 . Find the speeds of \(A\) and \(B\) after they collide. Sphere \(B\) now strikes a wall that is perpendicular to its path, rebounds and collides with \(A\) again. The coefficient of restitution between \(B\) and the wall is \(e\). Given that the second collision between \(A\) and \(B\) brings \(A\) to rest, find \(e\).