| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | November |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Relative velocity: find resultant velocity (magnitude and/or direction) |
| Difficulty | Moderate -0.5 The question text appears corrupted/incomplete, but based on the topic (Vectors Introduction & 2D) and module (M2 Mechanics), this likely involves basic 2D vector operations with velocities. Standard M2 vector questions involving velocity vectors are typically straightforward applications of vector addition/subtraction and basic mechanics, making them slightly easier than average A-level questions. |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.4gd = 32(d-0.8)^2/(2 \times 0.8)\) | M1 | PE/EE balance |
| \(20d^2 - 36d + 12.8 = 0\) | M1 | Solves 3 term quadratic |
| \(d = 1.31 \text{ m only}\) | A1 | [4] |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.4g(0.8 + e) = 32e^2/(2 \times 0.8)\) | M1 | PE/EE balance |
| \(20e^2 - 4e + 3.2 = 0\) | A1 | |
| \(e = 0.5(1)\) (also \(-3.12\)) | M1 | Solves 3 term quadratic |
| \(d = 1.31 \text{ m only}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.4v^2/2\) | A1 | |
| \(= 0.4g \times 1 - 32(1-0.8)^2/(2 \times 0.8)\) | ||
| \(v = 4 \text{ ms}^{-1}\) | A1 | [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Rebound \(v = 0.8\) | B1ft | \(\text{flcv}(v(\text{ii}) = \sqrt{(1-0.96)} = 0.2v(\text{ii})\) |
| \(0 = 0.4 \times 0.8^2/2 + 32 \times 0.2^2/1.6 - 0.4gh\) | M1 | EE/PE/KE balance, \(h = 0.232\) |
| \(OP (=1-h) = 0.768 \text{ m}\) | A1 | [3] |
**(i)**
$0.4gd = 32(d-0.8)^2/(2 \times 0.8)$ | M1 | PE/EE balance
$20d^2 - 36d + 12.8 = 0$ | M1 | Solves 3 term quadratic
$d = 1.31 \text{ m only}$ | A1 | [4] | Other value $0.4876..$
**OR**
$0.4g(0.8 + e) = 32e^2/(2 \times 0.8)$ | M1 | PE/EE balance
$20e^2 - 4e + 3.2 = 0$ | A1 |
$e = 0.5(1)$ (also $-3.12$) | M1 | Solves 3 term quadratic
$d = 1.31 \text{ m only}$ | A1 |
**(ii)**
$0.4v^2/2$ | A1 |
$= 0.4g \times 1 - 32(1-0.8)^2/(2 \times 0.8)$ | |
$v = 4 \text{ ms}^{-1}$ | A1 | [3]
**(iii)**
Rebound $v = 0.8$ | B1ft | $\text{flcv}(v(\text{ii}) = \sqrt{(1-0.96)} = 0.2v(\text{ii})$
$0 = 0.4 \times 0.8^2/2 + 32 \times 0.2^2/1.6 - 0.4gh$ | M1 | EE/PE/KE balance, $h = 0.232$
$OP (=1-h) = 0.768 \text{ m}$ | A1 | [3] | [10]$A$ has velocity $\vec{x}$
\begin{enumerate}[label=(\alph*)]
\item
\begin{enumerate}[label=(\roman*)]
\item $C$
\end{enumerate}
\item $A$ has velocity $\vec{x}$
\begin{enumerate}[label=(\roman*)]
\item $C$
\end{enumerate}
\item $C$ with velocities $v \vec{v}$
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2013 Q7}}