1
\begin{enumerate}[label=(\alph*)]
\item Roger of mass 70 kg and Sheuli of mass 50 kg are skating on a horizontal plane containing the standard unit vectors $\mathbf { i }$ and $\mathbf { j }$. The resistances to the motion of the skaters are negligible. The two skaters are locked in a close embrace and accelerate from rest until they reach a velocity of $2 \mathrm { ims } ^ { - 1 }$, as shown in Fig. 1.1.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{5dd6ba0d-e516-4b9e-ba19-6e90520b171b-002_191_181_543_740}
\captionsetup{labelformat=empty}
\caption{Fig. 1.1}
\end{center}
\end{figure}

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{5dd6ba0d-e516-4b9e-ba19-6e90520b171b-002_177_359_589_1051}
\captionsetup{labelformat=empty}
\caption{Fig. 1.1}
\end{center}
\end{figure}
\begin{enumerate}[label=(\roman*)]
\item What impulse has acted on them?

During a dance routine, the skaters separate on three occasions from their close embrace when travelling at a constant velocity of $2 \mathrm { i } \mathrm { ms } ^ { - 1 }$.
\item Calculate the velocity of Sheuli after the separation in the following cases.\\
(A) Roger has velocity $\mathrm { ims } ^ { - 1 }$ after the separation.\\
(B) Roger and Sheuli have equal speeds in opposite senses after the separation, with Roger moving in the $\mathbf { i }$ direction.\\
(C) Roger has velocity $4 ( \mathbf { i } + \mathbf { j } ) \mathrm { ms } ^ { - 1 }$ after the separation.
\end{enumerate}\item Two discs with masses 2 kg and 3 kg collide directly in a horizontal plane. Their velocities just before the collision are shown in Fig. 1.2. The coefficient of restitution in the collision is 0.5.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{5dd6ba0d-e516-4b9e-ba19-6e90520b171b-002_278_970_1759_594}
\captionsetup{labelformat=empty}
\caption{Fig. 1.2}
\end{center}
\end{figure}
\begin{enumerate}[label=(\roman*)]
\item Calculate the velocity of each disc after the collision.

The disc of mass 3 kg moves freely after the collision and makes a perfectly elastic collision with a smooth wall inclined at $60 ^ { \circ }$ to its direction of motion, as shown in Fig. 1.2.
\item State with reasons the speed of the disc and the angle between its direction of motion and the wall after the collision.
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{OCR MEI M2  Q1}}