Probability — practice question

Particles $P$ and $Q$, with masses $0.4\text{ kg}$ and $0.2\text{ kg}$ respectively, are fixed to the two ends of a light inextensible string. $P$ rests on a horizontal table, while the string runs over a small smooth pulley at the table’s edge. The string is stretched tight, and the section attached to $Q$ hangs vertically. The coefficient of friction between $P$ and the table is $0.5$. $Q$ is given a vertically downward speed of $5\text{ m s}^{-1}$, and after $t\text{ s}$ from the instant of projection the particles have speed $v\text{ m s}^{-1}$. Each particle experiences a resisting force of magnitude $0.9v\text{ N}$. Particle $P$ does not reach the pulley.