Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_40

2/40 A test projectile is fired horizontally into a viscous liquid with a velocity \(v_0\). The retarding force is proportional to the square of the velocity, so that the acceleration becomes \(a = -kv^2\). Derive expressions for the distance \(D\) traveled in the liquid and the corresponding time \(t\) required to reduce the velocity to \(v_0/2\). Neglect any vertical motion.