| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2012 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Speed at specific time or position |
| Difficulty | Standard +0.3 This is a standard projectiles question requiring application of energy conservation and kinematic equations. Part (i) is straightforward using v² = u² - 2as or energy methods. Part (ii) requires finding time and position components, but follows routine procedures. The 'speed increasing' condition guides students to the correct phase of motion. Slightly above average due to the two-part structure and coordinate geometry in part (ii), but all techniques are standard M2 material. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| \(v^2 = 17^2 - (30 \cos60)^2\) | M1 | Finds vertical speed |
| \(v = -8\) | A1 [2] | – may be implied by later work |
| Answer | Marks | Guidance |
|---|---|---|
| \(-8 = 30 \sin60 - gt\) | M1 | Finds relevant time |
| \(t = 3.4\) | A1 | 3.398 |
| \(y = [(30 \sin60)^2 - 8^2]/(2g) = (30.55)\) | B1 | Or \(y = (30 \sin60) \times 3.4 - g \cdot 3.4^2/2 = (30.53)\) |
| \(OP^2 = (30 \cos60 \times 3.4)^2 + 30.55^2\) | M1 | Use of Pythagoras |
| \(OP = 59.4 \, \text{m}\) | A1 [5] | Accept 59.5 |
## (i)
$v^2 = 17^2 - (30 \cos60)^2$ | M1 | Finds vertical speed
$v = -8$ | A1 [2] | – may be implied by later work
## (ii)
$-8 = 30 \sin60 - gt$ | M1 | Finds relevant time
$t = 3.4$ | A1 | 3.398
$y = [(30 \sin60)^2 - 8^2]/(2g) = (30.55)$ | B1 | Or $y = (30 \sin60) \times 3.4 - g \cdot 3.4^2/2 = (30.53)$
$OP^2 = (30 \cos60 \times 3.4)^2 + 30.55^2$ | M1 | Use of Pythagoras
$OP = 59.4 \, \text{m}$ | A1 [5] | Accept 59.5A particle $P$ is projected with speed $30$ m s$^{-1}$ at an angle of $60°$ above the horizontal from a point $O$ on horizontal ground. For the instant when the speed of $P$ is $17$ m s$^{-1}$ and increasing,
\begin{enumerate}[label=(\roman*)]
\item show that the vertical component of the velocity of $P$ is $8$ m s$^{-1}$ downwards, [2]
\item calculate the distance of $P$ from $O$. [5]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2012 Q5 [7]}}