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 } } }

$Provide an appropriate response. -If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to three times the square root of velocity, then the body's velocity t seconds into the fall satisfies the equation: \mathrm { m } \frac { \mathrm { dv } } { \mathrm { dt } } = \mathrm { mg } - 3 \mathrm { kv } ^ { 2 } where \mathrm { k } is a constant that depends on the body's aerodynamic properties and the density of the air. Determine the equilibrium, velocity curve, and the terminal velocity for a 150 \mathrm { lb } skydiver ( \mathrm { mg } = 150 ) with \mathrm { k } = 0 . A) Equilibrium: \mathrm { v } = \sqrt { \frac { \mathrm { mg } } { 3 \mathrm { k } } } \mathrm { v } _ { \text {terminal } } = 100 \mathrm { ft } / \mathrm { sec } B) Equilibrium: \mathrm { v } = \sqrt { \frac { \mathrm { mg } } { 3 \mathrm { k } } } \mathrm { v } _ { \text {terminal } } = 100 \mathrm { ft } / \mathrm { sec } C) Equilibrium: v = \sqrt { \frac { 3 \mathrm { k } } { \mathrm { mg } } } \mathrm { v } _ { \text {terminal } } = 100 \mathrm { ft } / \mathrm { sec } D) Equilibrium: v = \sqrt { \frac { 3 \mathrm { k } } { \mathrm { mg } } } v _ { \text {terminal } } = 100 \mathrm { ft } / \mathrm { sec }$