 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ia/paper-4/9c/c/iv/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

E = \frac{1}{2} u^{2} - \frac{2 mk}{a} .

Escape to infinity is possible exactly when

E \geq 0

. Thus the escape velocity criterion is

∣ u ∣ \geq 2 \frac{mk}{a} .

Equality corresponds to marginal escape.

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