For high speed motion through the air such as the skydiver

Last updated: 1/18/2023

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 kv2 dv dt mg 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 Assume the downward direction is positive Use k 0 for the constant of proportionality g 0 for acceleration due to gravity and v for v t