| Exam Board | Edexcel |
|---|---|
| Module | M5 (Mechanics 5) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Variable mass problems |
| Type | Rocket ascending against gravity |
| Difficulty | Challenging +1.8 This is a variable mass rocket equation problem from M5, requiring application of the rocket equation F = v_rel(dm/dt) + m(dv/dt), integration of a separable differential equation, and careful handling of signs. While the setup is given in part (a), students must understand momentum conservation for variable mass systems and perform non-trivial integration—topics beyond standard A-level but within Further Maths M5 scope. The mathematical techniques are accessible but the conceptual framework and multi-step nature make this significantly harder than average. |
| Spec | 6.03a Linear momentum: p = mv |
5. A rocket is launched vertically upwards from rest. Initially, the total mass of the rocket and its fuel is 1000 kg . The rocket burns fuel at a rate of $10 \mathrm {~kg} \mathrm {~s} ^ { - 1 }$. The burnt fuel is ejected vertically downwards with a speed of $2000 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ relative to the rocket, and burning stops after one minute. At time $t$ seconds, $t \leq 60$, after the launch, the speed of the rocket is $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Air resistance is assumed to be negligible.
\begin{enumerate}[label=(\alph*)]
\item Show that
$$- 9.8 ( 100 - t ) = ( 100 - t ) \frac { \mathrm { d } v } { \mathrm {~d} t } - 2000 .$$
\item Find the speed of the rocket when burning stops.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M5 Q5 [14]}}