Edexcel M2 2006 June — Question 5 8 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2006
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProjectiles
TypeTwo projectiles meeting - 2D flight
DifficultyStandard +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.
Spec3.02d 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,
  1. prove that \(\cos \alpha = \frac{4}{5}\). [4]
  1. Find the time which elapses between the instant when the stones are projected and the instant when they collide. [4]

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]}}