\includegraphics{figure_5}

A light elastic string has natural length $2$ m and modulus of elasticity $\lambda$ N. The ends of the string are attached to fixed points $A$ and $B$ which are at the same horizontal level and $2.4$ m apart. A particle $P$ of mass $0.6$ kg is attached to the mid-point of the string and hangs in equilibrium at a point $0.5$ m below $AB$ (see diagram).

\begin{enumerate}[label=(\roman*)]
\item Show that $\lambda = 26$. [4]
\end{enumerate}

$P$ is projected vertically downwards from the equilibrium position, and comes to instantaneous rest at a point $0.9$ m below $AB$.

\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Calculate the speed of projection of $P$. [5]
\end{enumerate}

\hfill \mbox{\textit{CAIE M2 2010 Q5 [9]}}