A ball of mass m is thrown upward with a velocity v. If air exerts an average resisting force F, the velocity with which the ball returns back to the thrower is

For upward motion, Retarding force = m g + F∴ Retardation a=mg+FmDistance s=V22a=V2m2(mg+F)For downward motion, force = m g - F∴ Acceleration a′=mg−FmDistance s′=v′22a′=v′2m2(mg−F)Since s′=s, v′2mg−F=v2mg+F∴ v′=vmg−Fmg+F