Particles $P$ and $Q$, having masses $0.3\,\text{kg}$ and $0.2\,\text{kg}$ respectively, are initially at rest on a smooth horizontal plane. $P$ is sent off at a speed of $4\,\text{m s}^{-1}$ directly towards $Q$. Once $P$ and $Q$ collide, $Q$ starts to move with a speed of $3\,\text{m s}^{-1}$.
(a)[2]
Determine the speed of $P$ after the collision.
(b)[2]
After the collision, $Q$ moves directly towards a third particle $R$, of mass $m\,\text{kg}$, which is stationary on the plane. The two particles $Q$ and $R$ coalesce on impact and move with a speed of $2\,\text{m s}^{-1}$. Determine $m$.
Worked solution & mark scheme
This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies conservation of momentum, e.g. $0.3\times4+0=0.3v+0.2\times3$” …