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Classical Mechanics

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Moderate

Terminal Speed: Linear Air Resistance

CLMECH-X67T$F

If the force of air resistance is equal to $k\, v$, what is the terminal speed of an object falling through the atmosphere?

Here $k$ is a constant specific to the falling object, and $v$ is the instantaneous speed.

Write a formula for the terminal speed, $v_T$, in terms of the acceleration of gravity, $g$, the mass of the object, $m$, and the force constant, $k$.

A

$$v_T = \frac{k}{m\,g}$$

B

$$v_T = m\,g\,k$$

C

$$v_T = \frac{m\,g}{k}$$