\includegraphics{figure_5}

Figure 5 shows two particles $A$ and $B$, of mass $2m$ and $4m$ respectively, connected by a light inextensible string. Initially $A$ is held at rest on a rough inclined plane which is fixed to horizontal ground. The plane is inclined to the horizontal at an angle $\alpha$, where $\tan\alpha = \frac{3}{4}$. The coefficient of friction between $A$ and the plane is $\frac{1}{4}$. The string passes over a small smooth pulley $P$ which is fixed 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 and $B$ hangs vertically below $P$. The system is released from rest with the string taut, with $A$ at the point $X$ and with $B$ at a height $h$ above the ground.

For the motion until $B$ hits the ground,
\begin{enumerate}[label=(\alph*)]
\item give a reason why the magnitudes of the accelerations of the two particles are the same, [1]
\item write down an equation of motion for each particle, [4]
\item find the acceleration of each particle. [5]
\end{enumerate}

Particle $B$ does not rebound when it hits the ground and $A$ continues moving up the plane towards $P$. Given that $A$ comes to rest at the point $Y$, without reaching $P$,

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item find the distance $XY$ in terms of $h$. [6]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2013 Q7 [16]}}