| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Topic | Projectiles |
| Type | Projection from elevated point - angle above horizontal |
| Difficulty | Standard +0.3 This is a standard M2 projectiles question combined with kinematics involving integration. Part (a) uses standard SUVAT equations with projectile motion (5 marks suggests routine calculation). Parts (b-d) involve straightforward integration of acceleration to find velocity and position, then comparing distances. The 'show that' parts guide students to expected answers. While multi-part with 16 total marks, each component uses standard techniques without requiring novel insight or complex problem-solving. |
| Spec | 1.08d Evaluate definite integrals: between limits3.02f Non-uniform acceleration: using differentiation and integration3.02i Projectile motion: constant acceleration model |
\includegraphics{figure_2}
At time $t = 0$ a small package is projected from a point $B$ which is $2.4$ m above a point $A$ on horizontal ground. The package is projected with speed $23.75$ m s$^{-1}$ at an angle $α$ to the horizontal, where $\tan α = \frac{4}{5}$. The package strikes the ground at point $C$, as shown in Fig. 2. The package is modelled as a particle moving freely under gravity.
\begin{enumerate}[label=(\alph*)]
\item Find the time taken for the package to reach $C$.
[5]
\end{enumerate}
A lorry moves along the line $AC$, approaching $A$ with constant speed 18 m s$^{-1}$. At time $t = 0$ the rear of the lorry passes $A$ and the lorry starts to slow down. It comes to rest 7 seconds later. The acceleration, $a$ m s$^{-2}$ of the lorry at time $t$ seconds is given by
$$a = -\frac{1}{4}t^2, \quad 0 \leq t \leq 7.$$
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the speed of the lorry at time $t$ seconds.
[3]
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Hence show that $T = 6$.
[3]
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Show that when the package reaches $C$ it is just under 10 m behind the rear of the moving lorry.
[5]
\end{enumerate}
END
\hfill \mbox{\textit{Edexcel M2 Q7 [16]}}