| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2007 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | SUVAT in 2D & Gravity |
| Type | Vertical projection: time to ground |
| Difficulty | Moderate -0.8 This is a straightforward SUVAT problem with standard energy calculations. Part (a) is direct KE formula application, part (b) uses energy conservation (a 'show that' reduces difficulty), parts (c) and (d) are routine. The multi-step nature and energy approach add slight complexity, but all techniques are standard M2 fare with no problem-solving insight required. |
| Spec | 6.02d Mechanical energy: KE and PE concepts6.02e Calculate KE and PE: using formulae6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Kinetic energy = \(\frac{1}{2} \times 5 \times 10^2 = 250\) J | M1, A1 | Full method |
| Part (b): Using conservation of energy: KE when box hits ground = Initial KE + Change in potential energy = \(250 + 5 \times 30 \times g = 1720\) J | M1, A1ft, A1 | Could have sign errors; AG; SC2 \(5 \times 35.1 \times g = 1720\). ... |
| Part (c): \(\frac{1}{2}mv^2 = 1720\); \(v^2 = 688\); \(\therefore\) Speed is 26.2 m s\(^{-1}\) | M1, A1, A1 | CAO; accept \(\sqrt{688}\) or \(4\sqrt{43}\); SC2 26.3 |
| Part (d): No air resistance; Box is a particle | E1, E1 | Or no resistance forces; Deduct 1 mark for unacceptable third reason |
| Total: 10 |
| Answer/Working | Marks | Guidance |
|---|---|---|
| Kinetic energy = $\frac{1}{2} \times 5 \times 10^2 = 250$ J | M1, A1 | Full method |
| **Part (b):** Using conservation of energy: KE when box hits ground = Initial KE + Change in potential energy = $250 + 5 \times 30 \times g = 1720$ J | M1, A1ft, A1 | Could have sign errors; AG; SC2 $5 \times 35.1 \times g = 1720$. ... |
| **Part (c):** $\frac{1}{2}mv^2 = 1720$; $v^2 = 688$; $\therefore$ Speed is 26.2 m s$^{-1}$ | M1, A1, A1 | CAO; accept $\sqrt{688}$ or $4\sqrt{43}$; SC2 26.3 |
| **Part (d):** No air resistance; Box is a particle | E1, E1 | Or no resistance forces; Deduct 1 mark for unacceptable third reason |
| | | **Total: 10** |1 A hot air balloon moves vertically upwards with a constant velocity. When the balloon is at a height of 30 metres above ground level, a box of mass 5 kg is released from the balloon.
After the box is released, it initially moves vertically upwards with speed $10 \mathrm {~ms} ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Find the initial kinetic energy of the box.
\item Show that the kinetic energy of the box when it hits the ground is 1720 J .
\item Hence find the speed of the box when it hits the ground.
\item State two modelling assumptions which you have made.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2007 Q1 [10]}}