A marble of mass m falls through a fluid and is subject to the drag force F=-Av, where v is the velocity of the marble. The marble will reach a terminal speed given by v=(mg)/A. Use dimensional analysis to estimate how long it will take to reach the terminal speed. (Hint: A characteristic "time" can be constructed from A, g, and m.)
The Attempt at a Solution
The units on A are F/v= (kg/s).
The units on g are m/(s^2).
The units on m are kg.
However, g is the only value with meters, so I don't know how I'm supposed to combine them and get time, unless it's just m/A, but then why did the book give a hint about using g? Thanks for the help.