1. The problem statement, all variables and given/known data A body of mass is projected with speed and moves under uniform gravity in a medium that exerts a resistance force of magnitude (i) mk*abs(v) or (ii) mK*(abs(v))^2 , where k and K are the positive constants and v is the velocity of the body. Gravity can be ignored. Determine the subsequent motion in each case . Verify motion the motion is bounded in case i , but not in case ii 2. Relevant equations F=D+L 3. The attempt at a solution for case i m*dv/dt= m*k*abs(v) applying seperation of variables, I get dv/abs(v)=kdt ==> ln(abs(v))=kt ===> v=Ce^-kt or v=Ce^kt , C being a constant and v depending on whether or not is positive or negative. for case two, my physical system is the quadratic resistance dv/dt=mk*(abs(v))^2 applying once again the seperation of variables method I get: -1/K*1/v=t ==> v=-1/kt+C I don't understand how to verify that the body is bounded. I know that a body is bounded if it cannot overcome its gravitional potential energy. I don't understand how I can possibly ignore gravity , unless the body is completely immersed in a vacuum and that cannot be possible if a fluid force is exerting a force on the object.