1. Two particles $P$ and $Q$, with masses 0.4 kg and 2.4 kg respectively, are moving in the same direction along a straight line on a smooth horizontal plane. At the instant when $P$ has speed $10m{s}^{-1}$ and $Q$ has speed $um{s}^{-1}$, the two particles collide directly. Immediately after the collision, the two particles are moving in opposite directions and the speed of $P$ is half of the speed of $Q$.

Show that the speed of $Q$ immediately after the collision is $\frac{2}{11}(10+6u)m{s}^{-1}$