A Terminal Velocity

At terminal velocity, $F_{\text{net}}=0$. Thus the drag force on the skydiver must equal the force of gravity (the person’s weight). Using the equation of drag force, we find $\text{mg}=\frac{1}{2}{\text{ρCAv}}^2$.

Thus the terminal velocity $v_{\mathrm{t}}$ can be written as

All quantities are known except the person’s projected area. This is an adult (85 kg) falling spread eagle. We can estimate the frontal area as

Using our equation for $v_{\text{t}}$, we find that

This result is consistent with the value for $v_{\text{t}}$ mentioned earlier. The 75-kg skydiver going feet first had a $v=\text{98 m}/\text{s}$. He weighed less but had a smaller frontal area and so a smaller drag due to the air.