c
The blob of mud would have a velocity of \(2 v\) and an initial height of \(2 r .\) Thus time of travel \(t\) is given using \(s=u t+\frac{1}{2} a t^{2}\) or \(2 r=\frac{1}{2} g t^{2}\)

\(t=2 \sqrt{\frac{r}{g}}\)

Thus distance \(\mathrm{AB}\) is given as \(2 v t=4 v \sqrt{\frac{r}{g}}\)