A sledge and a child sitting on it have a combined mass of 29.5 kg. The sledge slides on horizontal ice with negligible resistance to its movement.

\begin{enumerate}[label=(\roman*)]
\item While at rest, the sledge is hit directly from behind by a ball of mass 0.5 kg travelling horizontally at $10 \text{ m s}^{-1}$. The coefficient of restitution in the collision is 0.8. After the impact the speeds of the sledge and the ball are $V_1 \text{ m s}^{-1}$ and $V_2 \text{ m s}^{-1}$ respectively.

Calculate $V_1$ and $V_2$ and state the direction in which the ball is travelling after the impact. [7]

\item While at rest, the sledge is hit directly from behind by a snowball of mass 0.5 kg travelling horizontally at $10 \text{ m s}^{-1}$. The snowball sticks to the sledge.

\begin{enumerate}[label=(\Alph*)]
\item Calculate the velocity with which the combined sledge and snowball start to move. [3]

\item The child scoops up the 0.5 kg of snow and drops it over the back of the sledge. What happens to the velocity of the sledge? Give a reason for your answer. [2]
\end{enumerate}

\item In another situation, the sledge is travelling over the ice at $2 \text{ m s}^{-1}$ with 10.5 kg of snow on it (giving a total mass of 40 kg). The child throws a snowball of mass 0.5 kg from the sledge, parallel to the ground and in the positive direction of the motion of the sledge. Immediately after the snowball is thrown, the sledge has a speed of $V \text{ m s}^{-1}$ and the snowball and sledge are separating at a speed of $10 \text{ m s}^{-1}$.

Draw a diagram showing the velocities of the sledge and snowball before and after the snowball is thrown.

Calculate $V$. [5]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI M2 2007 Q1 [17]}}