Units Mismatch in Analytical Mechanics Textbook

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The discussion centers on a potential units mismatch in the terminal velocity equation from an Analytical Mechanics textbook. The equation presented for terminal velocity includes terms that appear inconsistent in their units. However, it is clarified that the constants c1 and c2 derive from the drag force expression, where c1 has units of Mass/Time and c2 has units of Mass/Length. When these units are analyzed, they align correctly, confirming that the equation is valid and the units do match. The initial concern about the mismatch is resolved through this unit analysis.
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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

vt=[(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.
 
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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.
 
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