Drag Force¶
If we fall in air, the air pushes back. This air resistance is approximately proportional to the square of objects speed:
\[
F_D = Dv^2
\]
D is proportionality constant depending on the objects shape and air density
After falling we reach terminal velocity. By second newtons law this is defined as:
\[\begin{split}
\sum F_y = ma_y \\
mg - Dv_y^2 = ma_y
\end{split}\]
Since at terminal velocity the acceleration \(a_y = 0\) (do not accelerate) we get:
\[\begin{split}
mg - Dv_y^2 = 0 \\
v_t = \sqrt{\frac{mg}{D}}
\end{split}\]