For high-speed motion through the air—such as the skydiver shown in the figure below falling before the parachute is opened—air

high-speed-motion
skydiver

#1

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:

image