**For high-speed motion through the air—such as the skydiver shown in the figure below falling before the parachute is opened—air resistance is closer to a power of the instantaneous velocity**

v(t).

Determine a differential equation for the velocity

v(t)

of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity. (Use

k > 0

for the constant of proportionality,

g > 0

for acceleration due to gravity, and v for

v(t).)

**Answer:**