A test projectile is fi red horizontally into a viscous liquid with a velocity v 0 .

Question:

A test projectile is fi red horizontally into a viscous liquid with a velocity v₀. The retarding force is proportional to the square of the velocity, so that the acceleration becomes a = −kv². Derive expressions for the distance D traveled in the liquid and the corresponding time t required to reduce the velocity to v₀/2. Neglect any vertical motion.