| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2006 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Two projectiles meeting - 2D flight |
| Difficulty | Standard +0.3 This is a standard M2 projectiles problem requiring systematic application of SUVAT equations to two projectiles. Part (a) involves equating horizontal displacements to find cos α (a 3-4-5 triangle), and part (b) requires equating vertical positions. The problem is methodical rather than insightful, with clear structure and standard techniques, making it slightly easier than average for M2. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02i Projectile motion: constant acceleration model |
A vertical cliff is 73.5 m high. Two stones $A$ and $B$ are projected simultaneously. Stone $A$ is projected horizontally from the top of the cliff with speed 28 m s$^{-1}$. Stone $B$ is projected from the bottom of the cliff with speed 35 m s$^{-1}$ at an angle $\alpha$ above the horizontal. The stones move freely under gravity in the same vertical plane and collide in mid-air. By considering the horizontal motion of each stone,
\begin{enumerate}[label=(\alph*)]
\item prove that $\cos \alpha = \frac{4}{5}$.
[4]
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the time which elapses between the instant when the stones are projected and the instant when they collide.
[4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2006 Q5 [8]}}