| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Horizontal projection from height |
| Difficulty | Standard +0.3 This is a standard M2 projectile motion question with straightforward application of SUVAT equations. Parts (a)-(d) involve routine calculations with vertical motion under gravity and Pythagoras' theorem for resultant velocity. Part (e) tests understanding that time is independent of horizontal velocity. Part (f) requires recognizing air resistance limitations of the particle model. While multi-part with 16 marks total, each component uses well-practiced techniques without requiring novel insight or complex problem-solving, making it slightly easier than average. |
| Spec | 3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(600 = \frac{1}{2}gt^2\) | \(t = \sqrt{122.45} = 11.1 \text{ s}\) | M1 A1 A1 |
| (b) \(x = 55t = 608.6 \text{ m}\) | M1 A1 | |
| (c) \(v_x = 55\), \(v_y = gt = 108.4\) | \(v = \sqrt{v_x^2 + v_y^2} = \sqrt{14785} = 121.6\) | M1 A1 M1 A1 |
| \(121.6 < 125\) so packet does not split open | A1 | |
| (d) Need \(v_x^2 + 108.4^2 = 125^2 = 15625\) so \(v_x = 62.2 \text{ ms}^{-1}\) | M1 A1 A1 | |
| (e) \(11.1 \text{ s}\), as in (a) | A1 | |
| (f) Leaflet is likely to drift due to wind and air resistance, so particle model is not appropriate | B1 B1 | 16 marks |
**(a)** $600 = \frac{1}{2}gt^2$ | $t = \sqrt{122.45} = 11.1 \text{ s}$ | M1 A1 A1 |
**(b)** $x = 55t = 608.6 \text{ m}$ | M1 A1 |
**(c)** $v_x = 55$, $v_y = gt = 108.4$ | $v = \sqrt{v_x^2 + v_y^2} = \sqrt{14785} = 121.6$ | M1 A1 M1 A1 |
$121.6 < 125$ so packet does not split open | A1 |
**(d)** Need $v_x^2 + 108.4^2 = 125^2 = 15625$ so $v_x = 62.2 \text{ ms}^{-1}$ | M1 A1 A1 |
**(e)** $11.1 \text{ s}$, as in (a) | A1 |
**(f)** Leaflet is likely to drift due to wind and air resistance, so particle model is not appropriate | B1 B1 | 16 marksAn aeroplane, travelling horizontally at a speed of 55 ms$^{-1}$ at a height of 600 metres above horizontal ground, drops a sealed packet of leaflets. Find
\begin{enumerate}[label=(\alph*)]
\item the time taken by the packet to reach the ground, [3 marks]
\item the horizontal distance moved by the packet during this time. [2 marks]
\end{enumerate}
The packet will split open if it hits the ground at a speed in excess of 125 ms$^{-1}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Determine, with explanation, whether the packet will split open. [5 marks]
\item Find the lowest speed at which the aeroplane could be travelling, at the same height of 600 m, to ensure that the packet will split open when it hits the ground. [3 marks]
\end{enumerate}
One of the leaflets is stuck to the front of the packet and becomes detached as it leaves the aeroplane.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{4}
\item If the leaflet is modelled as a particle, state how long it takes to reach the ground. [1 mark]
\item Comment on the model of the leaflet as a particle. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q8 [16]}}