We solve for the motion of an object with initial velocity v[subscript 0] and subject only to the combined drag of forces linear and quadratic in the velocity. This problem was treated briefly by Newton, after he developed a theoretical argument for the quadratic term, which we now know is characteristic of turbulent flow. Linear drag introduces a time [tau], and the two drag forces are equal at a critical velocity v[subscript c]; this defines a characteristic distance R = v[subscript c][tau]; details are discussed for spheres and for cylinders moving along their axis. For v[subscript 0]/v[subscript c] [approximately] 1 the role of quadratic drag is largely to reduce the velocity to v[subscript c], below which linear drag dominates. The penetration length is given by L[subscript N] = Rln(1 + v[subscript 0]/v[subscript c]). As noted by Gamow, L[subscript N] is relevant to the range of non-self-propelled projectiles, such as artillery shells, bullets, ground penetration bombs and spears shot from spearguns; it is also relevant to windmills and fans. (Contains 6 footnotes.)