(Solved): 4. A test projectile is fired horizontally into a viscous liquid with a velocity v0. The ret ...

4. 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 $$a=?k{v}^2$$. 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. $$\left[0.693/k,1/\left(k{v}_0\right)\right]$$