Provide an Appropriate Response $m$ Falling from Rest Under the Action of Gravity Encounters an Falling

Multiple Choice

Provide an appropriate response.
-If a body of mass $m$ falling from rest under the action of gravity encounters an air resistance proportional to three times the square root of velocity, then the body's velocity $t$ seconds into the fall satisfies the equation: $\mathrm { m } \frac { \mathrm { dv } } { \mathrm { dt } } = \mathrm { mg } - 3 \mathrm { kv } ^ { 2 }$ where $\mathrm { k }$ is a constant that depends on the body's aerodynamic properties and the density of the air.
Determine the equilibrium, velocity curve, and the terminal velocity for a $150 \mathrm { lb }$ skydiver $( \mathrm { mg } = 150 )$ with $\mathrm { k } = 0$ .

A) Equilibrium: $\mathrm { v } = \sqrt { \frac { \mathrm { mg } } { 3 \mathrm { k } } }$

$\mathrm { v } _ { \text {terminal } } = 100 \mathrm { ft } / \mathrm { sec }$

B) Equilibrium: $\mathrm { v } = \sqrt { \frac { \mathrm { mg } } { 3 \mathrm { k } } }$

$\mathrm { v } _ { \text {terminal } } = 100 \mathrm { ft } / \mathrm { sec }$

C) Equilibrium: $v = \sqrt { \frac { 3 \mathrm { k } } { \mathrm { mg } } }$

$\mathrm { v } _ { \text {terminal } } = 100 \mathrm { ft } / \mathrm { sec }$

D) Equilibrium: $v = \sqrt { \frac { 3 \mathrm { k } } { \mathrm { mg } } }$

$v _ { \text {terminal } } = 100 \mathrm { ft } / \mathrm { sec }$