A baseball is dropped form the roof of a tall building. As the ball falls, the air exert a
resistive force (f) that varies directly with the speed as f = qv, where q is a constant.
Find the speed of the falling ball as a function of time

 here we can consider the assistance post to be a frictional force or some kind of resistance force which is proportional to the velocity so here the net force at political instant on the body will be the gravitational force - the resistance force that is the net force on the body and we know that the net force on the body is equal to mass into acceleration of the body and you very well known that that acceleration of is Gravitation force - resistance force is equal to mass ×differential of velocity if you write it is an equation and take the MG - q v part into the denominator ofdv and dt to right  then you can integrate it to have an expression in logarithm as velocity as a variable

 

ok, so the final equation looks like mg-qv=mdv/dt? also i am not that good in integrations,  can you do it please?

I don't know how to upload an image here.    so that I can show you how it's done. 

   if you tell me then. .......

the motion of ball will follow equation:  m*a = m*g-f                 m is mass of ball

or                                                          m*a = m*g-q*v,

 

                                                                 

                                                        

integrating equation , take initial v = 0