| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2018 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Projectile on inclined plane |
| Difficulty | Standard +0.8 This is a challenging projectile motion problem requiring coordinate transformation between horizontal/vertical and inclined plane systems. Students must resolve velocity at 60° to horizontal (15° above 45° slope), find impact time by relating x and y via the plane equation y=x-tan(45°), then transform to perpendicular distance from plane. The multi-step coordinate geometry and non-standard angle make this significantly harder than typical projectile questions. |
| Spec | 3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model |
\includegraphics{figure_7}
A small object is projected with speed $24\text{ m s}^{-1}$ from a point $O$ at the foot of a plane inclined at $45°$ to the horizontal. The angle of projection of the object is $15°$ above a line of greatest slope of the plane (see diagram). At time $t\text{ s}$ after projection, the horizontal and vertically upwards displacements of the object from $O$ are $x\text{ m}$ and $y\text{ m}$ respectively.
\begin{enumerate}[label=(\roman*)]
\item Express $x$ and $y$ in terms of $t$, and hence find the value of $t$ for the instant when the object strikes the plane. [4]
\item Express the vertical height of the object above the plane in terms of $t$ and hence find the greatest vertical height of the object above the plane. [5]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2018 Q7 [9]}}