Moderate -0.8 This is a straightforward M1 momentum question testing direct application of conservation of momentum (part a) and impulse-momentum theorem (part b). Both parts are standard textbook exercises requiring only routine substitution into formulas with no problem-solving insight or geometric complexity needed.
Two particles \(A\) and \(B\), of mass \(3\) kg and \(2\) kg respectively, are moving in the same direction on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of \(A\) is \(4 \text{ m s}^{-1}\) and the speed of \(B\) is \(1.5 \text{ m s}^{-1}\). In the collision, the particles join to form a single particle \(C\).
Find the speed of \(C\) immediately after the collision. [3]
Two particles \(P\) and \(Q\) have mass \(3\) kg and \(m\) kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table. Each particle has speed \(4 \text{ m s}^{-1}\), when they collide directly. In this collision, the direction of motion of each particle is reversed. The speed of \(P\) immediately after the collision is \(2 \text{ m s}^{-1}\) and the speed of \(Q\) is \(1 \text{ m s}^{-1}\). Find
the value of \(m\), [3]
the magnitude of the impulse exerted on \(Q\) in the collision. [2]
\begin{enumerate}[label=(\alph*)]
\item Two particles $A$ and $B$, of mass $3$ kg and $2$ kg respectively, are moving in the same direction on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of $A$ is $4 \text{ m s}^{-1}$ and the speed of $B$ is $1.5 \text{ m s}^{-1}$. In the collision, the particles join to form a single particle $C$.
Find the speed of $C$ immediately after the collision. [3]
\item Two particles $P$ and $Q$ have mass $3$ kg and $m$ kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table. Each particle has speed $4 \text{ m s}^{-1}$, when they collide directly. In this collision, the direction of motion of each particle is reversed. The speed of $P$ immediately after the collision is $2 \text{ m s}^{-1}$ and the speed of $Q$ is $1 \text{ m s}^{-1}$. Find
\begin{enumerate}[label=(\roman*)]
\item the value of $m$, [3]
\item the magnitude of the impulse exerted on $Q$ in the collision. [2]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2006 Q2 [8]}}