Answer to Question #272950 in Mechanics | Relativity for alistar

Question

 A ball is dropped from rest and feels air resistance as it falls. Which of the graphs in Fig. Q5.26 best represents its vertical

velocity component as a function of time?

Answer 1

air resistance depends on v², so equation of motion:

$ma=mg-kv^2$

$mv'=mg-kv^2$

$\frac{mdv}{mg-kv^2}=dt$

solution is:

$arctan(k_1v)=k_2t+k$

or

$v=tan(k_2t+k)/k_1$

Answer: c