May/June 2026 Paper 43

Particles $P$ and $Q$ have masses $2\mathrm{kg}$ and $5\mathrm{kg}$ respectively. The particles are initially held at rest $3\mathrm{m}$ apart on the same line of greatest slope of a rough plane. The plane is inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha =0.28$ (see diagram). The coefficient of friction between $P$ and the plane and the coefficient of friction between $Q$ and the plane are both $0.2$. Particle $P$ is projected directly towards $Q$ with speed $8m/s$. At the same instant, $Q$ is projected directly towards $P$ with speed $um/s$. The particles collide $0.25\mathrm{s}$ after they are projected.