The terminal velocity \( V_t \) of an object falling through a fluid can be described by the equation:
\[ V_t = \sqrt{\frac{2mg}{\rho C_d A}} \]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity,
- \( \rho \) is the density of the fluid,
- \( C_d \) is the drag coefficient,
- \( A \) is the cross-sectional area of the object.
None of the options provided directly match this correct formulation. However, if we simplify and rearrange terms involving \( w \) (weight), where \( w = mg \), we can derive:
\[ V_t = \sqrt{\frac{2w}{\rho C_d A}} \]
If you can clarify or provide the correct context for the variables involved or if there are specific units or relationships defined, I might be able to provide further assistance in identifying the closest match.
1 answer