Separable Differential Equations: Videos & Practice Problems

A skydiver is descending under the influence of gravity and air resistance. According to Newton's Second Law of Motion, the velocity $v\left(t\right)$ of the skydiver satisfies the equation $m\cdot v^{\prime }\left(t\right)=mg+R\left(v\right)$, where $m$ is the mass of the skydiver, $g$ is the acceleration due to gravity, and $R\left(v\right)$ represents the resistive force due to air drag. Assume the resistive force is proportional to the square of the velocity and acts opposite to the direction of motion, so $R\left(v\right)=-c{v}^2$, where $c>0$ is the drag coefficient. Suppose the positive direction is downward. Find the velocity function $v\left(t\right)$ assuming $v\left(0\right)=0$, and that the velocity satisfies the condition .