| Exam Board | OCR MEI |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2008 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Variable mass problems |
| Type | Rocket in deep space, no gravity |
| Difficulty | Challenging +1.2 This is a standard variable mass rocket equation derivation from M4/Further Mechanics. Part (i) is a bookwork 'show that' requiring application of the rocket equation formula, part (ii) is straightforward separation of variables and integration, and part (iii) is direct substitution. While the topic is Further Maths content (making it inherently harder than pure A-level), this is a textbook exercise with no novel insight required, following a well-rehearsed method. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.06a Variable force: dv/dt or v*dv/dx methods |
1 A rocket in deep space starts from rest and moves in a straight line. The initial mass of the rocket is $m _ { 0 }$ and the propulsion system ejects matter at a constant mass rate $k$ with constant speed $u$ relative to the rocket. At time $t$ the speed of the rocket is $v$.\\
(i) Show that while mass is being ejected from the rocket, $\left( m _ { 0 } - k t \right) \frac { \mathrm { d } v } { \mathrm {~d} t } = u k$.\\
(ii) Hence find an expression for $v$ in terms of $t$.\\
(iii) Find the speed of the rocket when its mass is $\frac { 1 } { 3 } m _ { 0 }$.
\hfill \mbox{\textit{OCR MEI M4 2008 Q1 [12]}}