a particle of unit mass falls from rest, under gravity, in a medium in which there is a resistance of magnitude gv^2/U^2, wher v is the speed of the particle after time t and u is a positive constant. show that 2gt=U ln(U+v/U-v).

Question

anonymous · Answer

Apply Newtons 2nd law.

$$m(d ^{2}x/dt ^{2}) = mg-V ^{2}/U ^{2}$$  
we also know
$$d ^{2}x/dt ^{2} = dV/dt$$  set m=1

 substitute into newtons 2nd law and integrate (hint use a trigonometric substitution .

change of variable for V)