\includegraphics{figure_9}

One end of a light inextensible string is attached to a particle $A$ of mass 2 kg. The other end of the string is attached to a second particle $B$ of mass 2.5 kg. Particle $A$ is in contact with a rough plane inclined at $\theta$ to the horizontal, where $\cos \theta = \frac{4}{5}$. The string is taut and passes over a small smooth pulley $P$ at the top of the plane. The part of the string from $A$ to $P$ is parallel to a line of greatest slope of the plane. Particle $B$ hangs freely below $P$ at a distance 1.5 m above horizontal ground, as shown in the diagram.

The coefficient of friction between $A$ and the plane is $\mu$. The system is released from rest and in the subsequent motion $B$ hits the ground before $A$ reaches $P$. The speed of $B$ at the instant that it hits the ground is $1.2$ ms$^{-1}$.

\begin{enumerate}[label=(\alph*)]
\item For the motion before $B$ hits the ground, show that the acceleration of $B$ is $0.48$ ms$^{-2}$. [1]
\item For the motion before $B$ hits the ground, show that the tension in the string is $23.3$ N. [3]
\item Determine the value of $\mu$. [5]

After $B$ hits the ground, $A$ continues to travel up the plane before coming to instantaneous rest before it reaches $P$.

\item Determine the distance that $A$ travels from the instant that $B$ hits the ground until $A$ comes to instantaneous rest. [4]
\end{enumerate}

\hfill \mbox{\textit{OCR H240/03 2020 Q9 [13]}}