Chapter 3 - Motion in Two or Three Dimensions - Problems - Exercises - Page 99: 3.82

frame rate, $f\geq23000 \space frames/s$, so option (c) is correct.

Let frame rate is $f$ frames/s, then time interval for one shot, $\Delta t=\frac{1}{f}\space s$. In that interval speed can travel maximum distance of $0.20 \space mm$. So, $v_{max}\Delta t=4.6\times\frac{1}{f}\leq0.20\times10^{-3}\Rightarrow f\geq\frac{4.6}{0.20\times10^{-3}}\Rightarrow f\geq23000 \space frames/s$.