| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2002 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Horizontal projection from height |
| Difficulty | Moderate -0.3 This is a standard two-part projectiles question requiring kinematic equations for horizontal projection and basic trajectory analysis. Part (i) involves routine application of s=ut and s=ut+½at² to find x and y, then eliminating t. Part (ii) requires finding time to hit sea level and calculating the angle using velocity components. All steps are textbook-standard with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| \(x = 10t, y = -5t^2\) | B1 | |
| Eliminates \(t\) to find an equation in \(x\) and \(y\) | M1 | |
| Obtains \(y = -x^2/20\) | A1 | 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Uses \(\tan\theta = dy/dx\) or \(\tan\theta = y/x\) | M1 | |
| Obtains \(x = 30\) when \(y = -45\) or \(t = 3\) when \(y = -45\) or \(x \geq 1\sigma\) and \(y = (∓)30\) | A1 | |
| Obtains angle as 108.4° (108.435) or 71.6° (71.565) | A1 | 3 marks |
**(i)**
$x = 10t, y = -5t^2$ | B1 |
Eliminates $t$ to find an equation in $x$ and $y$ | M1 |
Obtains $y = -x^2/20$ | A1 | 3 marks |
**(ii)**
Uses $\tan\theta = dy/dx$ or $\tan\theta = y/x$ | M1 |
Obtains $x = 30$ when $y = -45$ or $t = 3$ when $y = -45$ or $x \geq 1\sigma$ and $y = (∓)30$ | A1 |
Obtains angle as 108.4° (108.435) or 71.6° (71.565) | A1 | 3 marks |3\\
\includegraphics[max width=\textwidth, alt={}, center]{fcf239a6-6558-43ec-b404-70aa349af6a9-2_502_789_1742_680}
A stone is projected horizontally, with speed $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, from the top of a vertical cliff of height 45 m above sea level (see diagram). At time $t \mathrm {~s}$ after projection the horizontal and vertically upward displacements of the stone from the top of the cliff are $x \mathrm {~m}$ and $y \mathrm {~m}$ respectively.\\
(i) Write down expressions for $x$ and $y$ in terms of $t$, and hence obtain the equation of the stone's trajectory.\\
(ii) Find the angle the trajectory makes with the horizontal at the point where the stone reaches sea level.
\hfill \mbox{\textit{CAIE M2 2002 Q3 [6]}}