Units Mismatch in Analytical Mechanics Textbook

[shanepitts]

In my Analytical Mechanics textbook it states that the terminal velocity of a spherical object, whilst taking the linear and quadratic terms into consideration, is

v_t=[(mg/c₂)+(c₁/2c₂)²]^1/2-c₁/(2c₂)

The units don't seem to match here. Is this normal?

This is not a homework inquiry, it for personal reviewing.

 

[phyzguy]

Why don't they match? I think your c1 and c2 are from the expression Fdrag = c1 * v + c2 * v^2. Then the units of c1 are Mass/Time, and the units of c2 are Mass/Length. With these units, the units of c1/c2 is Length/Time, and the units of mg/c2 are Length^2/Time^2, and everything matches.