| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2006 |
| Session | January |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Projectile clearing obstacle |
| Difficulty | Standard +0.3 This is a standard M2 projectiles question requiring routine application of SUVAT equations in 2D. Parts (a)-(c) involve straightforward substitution into projectile motion formulas with no novel problem-solving required. Part (d) is a simple conceptual point about the target having physical size. Slightly easier than average due to the step-by-step scaffolding and standard techniques. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model |
| Answer | Marks |
|---|---|
| \(u_x = 11\cos 30°\) | B1 |
| \(\rightarrow 11\cos 30° \times t = 10\) \(\Rightarrow\) \(t = 1.05\) (s) cao | M1 A1 |
| Answer | Marks |
|---|---|
| \(s = 11\sin 30° \times t - 4.9t^2 \approx 0.37\) | B1 M1 A1 |
| \((2 - 1) - 0.37 = 0.63\) (m) | A1 |
| Answer | Marks |
|---|---|
| \(V\cos 30° \times t = 10\) \(\left(t = \frac{10}{V\cos 30°}\right)\) | M1 A1 |
| \(s = V\sin 30° \times \frac{10}{V\cos 30°} - \frac{4.9 \times 100}{V^2\cos^2\theta} - 1\) | M1 A1 |
| \(V^2 = 136.86\) | M1 |
| \(V \approx 12\) accept 11.7 | A1 |
| Answer | Marks |
|---|---|
| B and/or T are not particles (They have extension giving a range of answers) | B1 |
## (a)
$u_x = 11\cos 30°$ | B1 |
$\rightarrow 11\cos 30° \times t = 10$ $\Rightarrow$ $t = 1.05$ (s) cao | M1 A1 |
## (b)
$s = 11\sin 30° \times t - 4.9t^2 \approx 0.37$ | B1 M1 A1 |
$(2 - 1) - 0.37 = 0.63$ (m) | A1 |
## (c)
$V\cos 30° \times t = 10$ $\left(t = \frac{10}{V\cos 30°}\right)$ | M1 A1 |
$s = V\sin 30° \times \frac{10}{V\cos 30°} - \frac{4.9 \times 100}{V^2\cos^2\theta} - 1$ | M1 A1 |
$V^2 = 136.86$ | M1 |
$V \approx 12$ accept 11.7 | A1 |
## (d)
B and/or T are not particles (They have extension giving a range of answers) | B1 |\includegraphics{figure_3}
The object of a game is to throw a ball $B$ from a point $A$ to hit a target $T$ which is placed at the top of a vertical pole, as shown in Figure 3. The point $A$ is 1 m above horizontal ground and the height of the pole is 2 m. The pole is at a horizontal distance of 10 m from $A$. The ball $B$ is projected from $A$ with a speed of 11 m s$^{-1}$ at an angle of elevation of $30°$. The ball hits the pole at the point $C$. The ball $B$ and the target $T$ are modelled as particles.
\begin{enumerate}[label=(\alph*)]
\item Calculate, to 2 decimal places, the time taken for $B$ to move from $A$ to $C$. [3]
\item Show that $C$ is approximately 0.63 m below $T$. [4]
\end{enumerate}
The ball is thrown again from $A$. The speed of projection of $B$ is increased to $V$ m s$^{-1}$, the angle of elevation remaining $30°$. This time $B$ hits $T$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Calculate the value of $V$. [6]
\item Explain why, in practice, a range of values of $V$ would result in $B$ hitting the target. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2006 Q7 [14]}}