## Question 1:

### Part 1(a):

**Setup diagram:**
- $P$ has initial velocity $2u \rightarrow$, final velocity $\rightarrow v$
- $Q$ has initial velocity $\leftarrow u$, final velocity $\rightarrow y$
- Impulse $\frac{9mu}{2}$ acts leftward on $P$, rightward on $Q$

| Working/Answer | Mark | Guidance |
|---|---|---|
| Use of Impulse-momentum principle for $P$ | M1 | Condone sign errors but M0 if dimensionally incorrect e.g. if $m$ missing or $g$ included |
| $-\frac{9mu}{2} = 3m(v - 2u)$ | A1 | Correct unsimplified equation (may have $-v$) |
| $v = \frac{u}{2}$ | A1 | cao (must be positive) |
| | **(3)** | |

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### Part 1(b):

| Working/Answer | Mark | Guidance |
|---|---|---|
| Use of Impulse-momentum principle for $Q$, or CLM | M1 | Must use $2m$; condone sign errors but M0 if dimensionally incorrect. Or use of CLM, condone sign errors and consistent omission of $m$'s or consistent extra $g$'s, with their $v$. Must use correct masses on all four terms |
| $\frac{9mu}{2} = 2m(y - {-u})$ **OR** $3m \times 2u - 2mu = 3m \times \frac{u}{2} + 2my$ giving $y = \frac{5u}{4}$ | A1 | Correct unsimplified equation |
| Newton's Experimental Law | M1 | Use of NEL with their $v$ and their $y$; condone sign errors but M0 if ratio for $e$ is inverted |
| $e = \dfrac{\frac{5u}{4} - \frac{u}{2}}{2u + u}$ | A1 | |
| $e = \frac{1}{4}$ oe | A1 | |
| | **(5)** | |
| | **(8 marks total)** | |