May/June 2026 Paper 42

A particle $P$ is projected from a point $A$ with speed $4m/s$ up a line of greatest slope of a rough plane inclined at an angle $\theta$ to the horizontal, where $\tan \theta =\frac{4}{3}$. $P$ comes to instantaneous rest at a point $B$ on the plane (see diagram). The coefficient of friction between $P$ and the plane is $\frac{1}{3}$.