| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2010 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Basic trajectory calculations |
| Difficulty | Standard +0.2 This is a straightforward projectiles question requiring standard SUVAT equations and component resolution. Part (i) involves finding time from vertical motion, then calculating angle and height—routine mechanics. Part (ii) asks for range and time of flight using standard formulas. All steps are textbook exercises with no problem-solving insight required, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (i) tan α = 5/(26cos30°) | M1 |
| α = 12.5° (0.219rad) below the horizontal | A1 | Accept 77.5°/1.35rad with downward |
| Answer | Marks |
|---|---|
| 5 = (26sin30°) – 2gs | M1 |
| s = 7.2m | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| (ii) –(26sin30°) = (26sin30°) – gT | M1 | Or time to greatest height if later doubled |
| T = 2.6s | A1 | |
| OA = (26cos30°) × 2.6 = 58.5m | A1 | |
| [3] | 2 |
Question 2:
2 | (i) tan α = 5/(26cos30°) | M1
α = 12.5° (0.219rad) below the horizontal | A1 | Accept 77.5°/1.35rad with downward
vertical
2 2
5 = (26sin30°) – 2gs | M1
s = 7.2m | A1
[4]
(ii) –(26sin30°) = (26sin30°) – gT | M1 | Or time to greatest height if later doubled
T = 2.6s | A1
OA = (26cos30°) × 2.6 = 58.5m | A1
[3] | 2
Or B1 for OA = 26 sin(2 × 30°)/10 =
58.5A particle $P$ is projected with speed $26$ m s$^{-1}$ at an angle of $30°$ above the horizontal from a point $O$ on a horizontal plane.
\begin{enumerate}[label=(\roman*)]
\item For the instant when the vertical component of the velocity of $P$ is $5$ m s$^{-1}$ downwards, find the direction of motion of $P$ and the height of $P$ above the plane. [4]
\item $P$ strikes the plane at the point $A$. Calculate the time taken by $P$ to travel from $O$ to $A$ and the distance $OA$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2010 Q2 [7]}}