1.2 Physics DE

Falling ball

• Derive an equation for a falling object subject to air resistance

  • using newtons second law : $F=ma:a=\frac{dv}{dt}$
    • we find force of gravity, but we must find drag $\text{ assuming }{F}_d\alpha v:F_d=-\gamma v$
      • so we get that

$$\begin{array}{r}m\frac{dv}{dt}=F_{total}=F_g+F_d=mg-\gamma v⟹\frac{dv}{dt}g-\frac{\gamma }{m}v\end{array}$$