Moderate -0.3 This is a straightforward momentum conservation problem requiring students to apply conservation of momentum in one dimension and recognize that P can move in either direction after collision. The calculation is routine with clear given values, though the 'two possible outcomes' aspect (P rebounds or continues forward) adds minor complexity beyond the most basic collision questions.
1 Two particles \(P\) and \(Q\) of masses 0.2 kg and 0.5 kg respectively are at rest on a smooth horizontal plane. Particle \(P\) is projected with a speed \(6 \mathrm {~ms} ^ { - 1 }\) directly towards \(Q\). After \(P\) and \(Q\) collide, \(P\) moves with a speed of \(1 \mathrm {~ms} ^ { - 1 }\).
Find the two possible speeds of \(Q\) after the collision.
\includegraphics[max width=\textwidth, alt={}, center]{c3246fbe-6f77-48f7-98eb-19e9166008bc-02_2716_35_143_2012}
For attempt at use of conservation of momentum in at least one case. Must have three non-zero terms. Allow sign errors. Must have correct masses with relevant velocities. Their \(v\) may be in opposite direction.
Speed \(= 2 \text{ ms}^{-1}\)
A1
Do not allow negative.
Speed \(= 2.8[0] \text{ ms}^{-1}\) or \(\dfrac{14}{5} \text{ ms}^{-1}\) or \(2\dfrac{4}{5} \text{ ms}^{-1}\)
A1
OE. Do not allow negative.
[3]
## Question 1:
| Answer | Mark | Guidance |
|--------|------|----------|
| $0.2 \times 6 + 0 = 0.2 \times 1 + 0.5v$ or $0.2 \times 6 + 0 = 0.2 \times -1 + 0.5v$ | **M1** | For attempt at use of conservation of momentum in at least one case. Must have three non-zero terms. Allow sign errors. Must have correct masses with relevant velocities. Their $v$ may be in opposite direction. |
| Speed $= 2 \text{ ms}^{-1}$ | **A1** | Do not allow negative. |
| Speed $= 2.8[0] \text{ ms}^{-1}$ or $\dfrac{14}{5} \text{ ms}^{-1}$ or $2\dfrac{4}{5} \text{ ms}^{-1}$ | **A1** | OE. Do not allow negative. |
| | **[3]** | |
1 Two particles $P$ and $Q$ of masses 0.2 kg and 0.5 kg respectively are at rest on a smooth horizontal plane. Particle $P$ is projected with a speed $6 \mathrm {~ms} ^ { - 1 }$ directly towards $Q$. After $P$ and $Q$ collide, $P$ moves with a speed of $1 \mathrm {~ms} ^ { - 1 }$.
Find the two possible speeds of $Q$ after the collision.\\
\includegraphics[max width=\textwidth, alt={}, center]{c3246fbe-6f77-48f7-98eb-19e9166008bc-02_2716_35_143_2012}
\hfill \mbox{\textit{CAIE M1 2024 Q1 [3]}}