### Particle Dynamics and Newton's Laws

A body free-fall in a presence of a drag force in the form $\vec{F}_{drag}=-cv^2\hat{v}$ ,
where $c=Const$.

1. Draw the force diagram for the body during the free-fall.
2. Find the equation of motion of the body.
3. What is the terminal velocity, $v_t$, of the body. The terminal velocity reached when the body is in equilibrium.
4. Find the body velocity as a function of time. Assume $v(0)=0$.