Particles $P$ and $Q$ have masses $m\,\text{kg}$ and $2m\,\text{kg}$ respectively. Initially, they are both at rest and are $6.4\,\text{m}$ apart on the same line of greatest slope of a rough plane inclined at an angle $\alpha$ to the horizontal, where $\sin\alpha = 0.8$ (see diagram). Particle $P$ is released from rest and moves down the line of greatest slope. At the same time, particle $Q$ is projected up that same line of greatest slope with speed $10\,\text{m s}^{-1}$. The coefficient of friction between each particle and the plane is $0.6$.
(a)[4]
Show that the acceleration of $Q$ up the plane is $-11.6\,\text{m s}^{-2}$.
(b)[5]
Find the time for which the particles are in motion before they collide.
(c)[4]
The particles coalesce on impact. Find the speed of the combined particle immediately after the impact.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply Newton’s 2nd law to particle $Q$ to form equations along and perpendicular to plane” …