For high-speed motion through the air such as the skydiver shown in the following figure, falling before

Question:

For high-speed motion through the air €”such as the skydiver shown in the following figure, 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.

kv2 mg