| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2018 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Prism or block on inclined plane |
| Difficulty | Challenging +1.2 This is a projectile motion problem on an inclined plane requiring coordinate geometry and optimization. Part (i) involves resolving velocities at 60° to horizontal (45°+15°), writing parametric equations, and using the plane equation y=x to find impact time—straightforward but multi-step. Part (ii) requires expressing perpendicular distance to the plane and finding maximum via calculus. While requiring careful angle resolution and several techniques, it follows standard inclined plane projectile methodology without novel insight. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| 7(i) | x = (24cos60)t | B1 |
| y = (24sin60)t – gt 2/2 | B1 | Use vertical motion |
| (24cos60)t = (24sin60)t –gt 2/2 | M1 | Recognise that x = y |
| t = 1.76 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 7(ii) | h = (24sin60)t – gt 2/2 – (24cos60)t | B1 |
| M1 | Attempt to differentiate | |
| dh/dt = 24(sin60 – cos60) – gt | A1 | |
| 24(sin60 – cos60) – gt = 0, t = 0.878(46..) | M1 | Equate dh/dt = 0 to find t |
| h = 3.86 m | A1 |
Question 7:
--- 7(i) ---
7(i) | x = (24cos60)t | B1 | Use horizontal motion
y = (24sin60)t – gt 2/2 | B1 | Use vertical motion
(24cos60)t = (24sin60)t –gt 2/2 | M1 | Recognise that x = y
t = 1.76 | A1
4
--- 7(ii) ---
7(ii) | h = (24sin60)t – gt 2/2 – (24cos60)t | B1
M1 | Attempt to differentiate
dh/dt = 24(sin60 – cos60) – gt | A1
24(sin60 – cos60) – gt = 0, t = 0.878(46..) | M1 | Equate dh/dt = 0 to find t
h = 3.86 m | A1
5\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 $t$ s after projection, the horizontal and vertically upwards displacements of the object from $O$ are $x$ m and $y$ 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]}}