= Solution
For some orbital phase of the moon to permit an impact, the comet's planetocentric <hyperbolic Kepler orbit> must at least cross the moon's circular orbit. At the limiting case $a_m$ is the comet's <periapsis>, so the radial velocity in part (iv) vanishes. Consequently
$$
\boxed{b_{\max}=\frac{a_m}{\Delta v_{pc}}
\sqrt{\Delta v_{pc}^2+2v_m^2}
=a_m\sqrt{1+\frac{2v_m^2}{\Delta v_{pc}^2}}}.
$$
This is <gravitational focusing> by the planet; an actual collision additionally requires the moon to occupy the crossing point at the right time.
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