2. Two smooth spheres \(P\) and \(Q\) of equal radius and of mass \(2 m\) and \(5 m\) respectively, are moving towards each other along a horizontal straight line when they collide. After the collision, \(P\) and \(Q\) travel in opposite directions with speeds of \(3 \mathrm {~ms} ^ { - 1 }\) and \(4 \mathrm {~ms} ^ { - 1 }\) respectively. Given that the coefficient of restitution between the two particles is \(\frac { 1 } { 2 }\), find the speeds of \(P\) and \(Q\) before the collision.
(6 marks)

| Cons. of mom: $2mu_1 - 5mu_2 = ^7m(3) + 5m(4)$; $2u_1 - 5u_2 = 14$ | M1 A1 |
| $\frac{4-(-3)}{u_1+u_2} = \frac{1}{2}$ $\therefore u_1 + u_2 = 14$ | M1 A1 |
| Solve simul. giving $u_1 = 12\text{ ms}^{-1}$, $u_2 = 2\text{ ms}^{-1}$ | M1 A1 | (6 marks total)

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2. Two smooth spheres $P$ and $Q$ of equal radius and of mass $2 m$ and $5 m$ respectively, are moving towards each other along a horizontal straight line when they collide. After the collision, $P$ and $Q$ travel in opposite directions with speeds of $3 \mathrm {~ms} ^ { - 1 }$ and $4 \mathrm {~ms} ^ { - 1 }$ respectively.

Given that the coefficient of restitution between the two particles is $\frac { 1 } { 2 }$, find the speeds of $P$ and $Q$ before the collision.\\
(6 marks)\\

\hfill \mbox{\textit{Edexcel M2  Q2 [6]}}