Challenging +1.8 This is a classic variable mass/rocket equation problem requiring application of momentum conservation in the rocket's reference frame. Students must set up and integrate the differential equation dm/dt relating thrust to mass loss, which goes beyond standard M1-M3 content. The 7-mark allocation and need for calculus with changing mass makes this significantly harder than average, though it follows a well-established derivation pattern taught in M5.
A rocket propels itself by its engine ejecting burnt fuel. Initially the rocket has total mass \(M\), of which a mass \(kM\), \(k < 1\), is fuel. The rocket is at rest when its engine is started. The burnt fuel is ejected with constant speed \(c\), relative to the rocket, in a direction opposite to that of the rocket's motion. Assuming that there are no external forces, find the speed of the rocket when all its fuel has been burnt.
[7]
A rocket propels itself by its engine ejecting burnt fuel. Initially the rocket has total mass $M$, of which a mass $kM$, $k < 1$, is fuel. The rocket is at rest when its engine is started. The burnt fuel is ejected with constant speed $c$, relative to the rocket, in a direction opposite to that of the rocket's motion. Assuming that there are no external forces, find the speed of the rocket when all its fuel has been burnt.
[7]
\hfill \mbox{\textit{Edexcel M5 Q3 [7]}}