Past exam of the physics B course of the University of Cambridge / 2015 / Paper 2 / Section A / A5

Take upward as positive and interpret the stated $97\mathrm{kg}$ as the total mass immediately before launch, including the harpoon. The remaining probe mass is $M=95.6\mathrm{kg}$. Conservation of momentum during the short firing interval givesThe harpoon speed used here is relative to the comet, as printed. From $v_{\mathrm{esc}}^2=2G{M}_c/R$, the near-surface gravitational acceleration isFor the near-surface recoil height with constant downward thrust, the upward motion has downward acceleration $a=g_c+F/M$. ThereforeSince $H/R\simeq 1.8\times 10^{-4}$, treating gravity as constant is consistent. This uses only the stated gravity and thrust after firing; a taut tether could reduce this free-flight height, but no tether length or elasticity is specified. If instead $97\mathrm{kg}$ meant the probe mass after firing, the pre-firing mass would be $98.4\mathrm{kg}$ and its momentum would leave the probe still moving downward, with no upward excursion. This illustrates nearly cancelling recoil momenta in payload ejection. The mass convention matters because the launch momenta nearly cancel.