| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Projectiles |
| Type | Basic trajectory calculations |
| Difficulty | Moderate -0.3 This is a standard M2 projectile motion question requiring application of SUVAT equations in 2D. Parts (a)-(c) involve routine calculations with given time of flight and range, using standard formulas. Part (d) is a basic modelling comment. Slightly easier than average due to straightforward setup and no geometric complications. |
| Spec | 3.02i Projectile motion: constant acceleration model |
| Answer | Marks |
|---|---|
| vert. disp. \(= 0\) \(\therefore 8u_x - \frac{1}{2}g(8)^2 = 0\) | M1 A1 |
| \(u_x = \frac{1}{2}g(8) = 4g\) | A1 |
| horiz. disp. \(= 24\) \(\therefore 8u_x = 24\) so \(u_x = 3\) | M1 A1 |
| Answer | Marks |
|---|---|
| initial speed \(= \sqrt{(4g)^2 + 3^2} = 39.3 \text{ ms}^{-1} \text{ (3sf)}\) | M1 A1 |
| Answer | Marks |
|---|---|
| max. ht. when vert. vel. \(= 0\) \(\therefore 0 = (4g)^2 - 2gs\) | M1 A1 |
| \(\therefore\) max. ht. \(= 8g = 78.4 \text{ m}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| e.g. small X-section, reasonable to treat as particle and ignore air res. but, significant loss of mass during flight \(\therefore\) model not very suitable | B3 | (13) |
**Part (a):**
vert. disp. $= 0$ $\therefore 8u_x - \frac{1}{2}g(8)^2 = 0$ | M1 A1 |
$u_x = \frac{1}{2}g(8) = 4g$ | A1 |
horiz. disp. $= 24$ $\therefore 8u_x = 24$ so $u_x = 3$ | M1 A1 |
**Part (b):**
initial speed $= \sqrt{(4g)^2 + 3^2} = 39.3 \text{ ms}^{-1} \text{ (3sf)}$ | M1 A1 |
**Part (c):**
max. ht. when vert. vel. $= 0$ $\therefore 0 = (4g)^2 - 2gs$ | M1 A1 |
$\therefore$ max. ht. $= 8g = 78.4 \text{ m}$ | A1 |
**Part (d):**
e.g. small X-section, reasonable to treat as particle and ignore air res. but, significant loss of mass during flight $\therefore$ model not very suitable | B3 | (13)
---5. A firework company is testing its new brand of firework, the Sputnik Special. One of the company's employees lights a Sputnik Special on a large area of horizontal ground and it takes off at a small angle to the vertical. After a flight lasting 8 seconds it lands at a distance of 24 metres from the point where it was launched.
The employee models the firework as a particle and ignores air resistance and any loss of mass which the Sputnik Special experiences.
Using this model, find for this flight of the Sputnik Special,
\begin{enumerate}[label=(\alph*)]
\item the horizontal and vertical components of the initial velocity,
\item the initial speed, correct to 3 significant figures,
\item the maximum height attained.
\item Comment on the suitability of the modelling assumptions made by the employee.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q5 [13]}}