Particles $P$, $Q$ and $R$ have masses $0.6\,\text{kg}$, $0.4\,\text{kg}$ and $0.8\,\text{kg}$ respectively, and they are initially at rest on a smooth horizontal plane in a straight line. The separation from $P$ to $Q$ is $3\,\text{m}$, and the separation from $Q$ to $R$ is also $3\,\text{m}$. Particle $P$ is then projected directly towards $Q$ with speed $3\,\text{m s}^{-1}$. Once $P$ and $Q$ have collided, $P$ goes on moving in the same direction with speed $1.5\,\text{m s}^{-1}$.
(a)[2]
Determine the speed of $Q$ immediately after the collision.
(b)[1]
In the next collision, $Q$ and $R$ stick together. Determine the speed of the merged particle after the collision.
(c)[4]
Find the time from the moment $P$ is first projected to the instant when $P$ collides with the combined particle.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “An attempt to use conservation of momentum with three non-zero terms.” …