 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2011/ia/paper-4/11b/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

Without dust collection,

d M = - d m

. The rocket equation reduces to

M d v = u d m = - u d M .

Integrating from

v = 0

M = M_{0}

gives

v = u lo g \frac{M _{0}}{M} .

This is the usual rocket equation with constant relative exhaust speed, valid while the mass remains positive and the prescribed ejection continues.

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