Particles $P$ and $Q$, with masses $m\,\text{kg}$ and $0.3\,\text{kg}$ respectively, are initially stationary on a smooth horizontal plane. $P$ is given a speed of $5\,\text{m s}^{-1}$ straight towards $Q$. After $P$ and $Q$ collide, $P$ continues in the same direction as before, but with speed $2\,\text{m s}^{-1}$.
(a)[2]
Find, in terms of $m$, the speed of $Q$ after the collision.
(b)[2]
Following that collision, $Q$ travels directly towards a third particle $R$, with mass $0.6\,\text{kg}$, which is stationary on the plane. $Q$ is brought to rest in the collision with $R$, and $R$ begins to move with a speed of $1.5\,\text{m s}^{-1}$. Find the value of $m$.
Worked solution & mark scheme
This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: “An attempt to apply conservation of momentum, for example $m\times5+0=m\times2+0.3v$.” …