= Solution
An upward <drag force> $F_D\ge0$ changes the <variable-mass system> equation to
$$
\dot v+\frac{3\mu}{r_0+\mu t}v=g-\frac{F_D}{m}.
$$
For an ordinary <drag force> increasing with positive <speed>, the new curve lies below the no-drag curve. It still starts with slope $g$ if $F_D=0$ at rest. The dashed curve illustrates <quadratic drag on a sphere with constant radial growth>, using $F_D=\tfrac12 C_D\rho_{\rm air}\pi r^2v^2$ with constant <drag coefficient> $C_D$ and air <mass density> $\rho_{\rm air}$. The equation for these <dimensionless quantities> is
$$
\frac{dw}{d\tau}=1-\frac{3w}{1+\tau}-\eta\frac{w^2}{1+\tau},\qquad\eta=\frac{3C_D\rho_{\rm air}gr_0}{8\rho\mu^2}>0.
$$
The figure uses $\eta=2$ solely to show the shape; it is not an additional datum of the paper.
There is a limitation to the usual <terminal velocity> sketch here. The examiner's commentary describes a curve approaching <terminal velocity>, but the paper maintains unbounded radius growth and specifies no drag law. A horizontal limit is justified if one additionally treats the radius as approximately fixed, or otherwise assumes a drag-to-mass ratio with a fixed limiting balance. With the growing radius and constant-$C_D$ <quadratic drag> just written, the late balance instead gives
$$
\boxed{w\sim\sqrt{\tau/\eta},\qquad v\sim\sqrt{\frac{8\rho g\mu}{3C_D\rho_{\rm air}}\,t}.}
$$
This curve flattens in the sense that its slope tends to zero, but its <speed> remains unbounded. Thus \b[a lower, more strongly flattening curve is warranted; a finite terminal speed requires an additional assumption]. The no-growth approximation gives the familiar finite value $v_T=\sqrt{8\rho gr/(3C_D\rho_{\rm air})}$ for a specified fixed radius.https://www.whatdotheyknow.com/request/natural_science_tripos_physics_e/response/2127325/attach/3/FOI%202022%20639%20Sullivan%20materials.pdf?cookie_passthrough=1#page=62[Examiner commentary, B7, released PDF page 62: the stated terminal-velocity expectation]{ref}
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