A skydiver of mass falls straight downward through the air

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A skydiver of mass

m

falls straight downward through the air. Positive velocity is defined to be downward. The gravitational force has magnitude

mg

, and air resistance exerts an upward force whose magnitude is proportional to the speed,

cv

, where

c>0

. Which of the following differential equations correctly relates the velocity

v(t)

to time

t

? (a)

\displaystyle \frac{dv}{dt}=g+\frac{c}{m}v

(b)

\displaystyle \frac{dv}{dt}=\frac{c}{m}v-g

(c)

\displaystyle \frac{dv}{dt}=g-\frac{c}{m}v

(d)

\displaystyle \frac{dv}{dt}=-g-\frac{c}{m}v