Standard +0.3 This is a standard momentum conservation problem with a straightforward constraint (equal speeds after collision). Students must consider two cases (same/opposite directions) and solve simultaneous equations using conservation of momentum and the given condition. The algebra is routine and the setup is a textbook exercise, making it slightly easier than average.
1 Two particles \(P\) and \(Q\), of masses 0.1 kg and 0.4 kg respectively, are free to move on a smooth horizontal plane. Particle \(P\) is projected with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) towards \(Q\) which is stationary. After \(P\) and \(Q\) collide, the speeds of \(P\) and \(Q\) are equal.
Find the two possible values of the speed of \(P\) after the collision.
**Question 1:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Attempt at use of conservation of momentum in one case | M1 | $0.1 \times 4 + 0 = 0.4v + 0.1v$ or $0.1 \times 4 + 0 = 0.4v + 0.1(-v)$ OE. Must have correct number of terms. Allow sign errors. |
| Speed $= 0.8$ $[\text{ms}^{-1}]$ or $\frac{4}{5}$ | A1 | Must be positive. Allow Max M1A1A0 if $g$ included with the masses. |
| Speed $= \frac{4}{3}$ $[\text{ms}^{-1}]$ Allow 1.33 | A1 | Must be positive. |
| | **3** | |
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1 Two particles $P$ and $Q$, of masses 0.1 kg and 0.4 kg respectively, are free to move on a smooth horizontal plane. Particle $P$ is projected with speed $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ towards $Q$ which is stationary. After $P$ and $Q$ collide, the speeds of $P$ and $Q$ are equal.
Find the two possible values of the speed of $P$ after the collision.\\
\hfill \mbox{\textit{CAIE M1 2023 Q1 [3]}}