Standard +0.3 This is a standard M2 collision problem requiring conservation of momentum and Newton's restitution law. While it involves algebraic manipulation with the constraint that P's direction reverses (v_P < 0), the approach is routine for M2 students and the inequality emerges naturally from the algebra. The 8 marks reflect working steps rather than conceptual difficulty.
A particle \(P\) of mass \(m\) is moving in a straight line on a smooth horizontal surface with speed \(4u\). The particle \(P\) collides directly with a particle \(Q\) of mass \(3m\) which is at rest on the surface. The coefficient of restitution between \(P\) and \(Q\) is \(e\). The direction of motion of \(P\) is reversed by the collision.
Show that \(e > \frac{1}{3}\). [8]
A particle $P$ of mass $m$ is moving in a straight line on a smooth horizontal surface with speed $4u$. The particle $P$ collides directly with a particle $Q$ of mass $3m$ which is at rest on the surface. The coefficient of restitution between $P$ and $Q$ is $e$. The direction of motion of $P$ is reversed by the collision.
Show that $e > \frac{1}{3}$. [8]
\hfill \mbox{\textit{Edexcel M2 2011 Q2 [8]}}