A test projectile is fired horizontally into a viscous liquid with a velocity u.The retarding force is propotional to the square of the velocity, so that the acceleration becomes a=-k(v)^2 . Derive expressions for the distance D travelled in the liquid and corresponding time t required to reduce the velocity to u/2.

Since the object is moving in horizontal through viscous solution therefore its acceleration will be slow down by both gravity towards the earth as well as viscous solution.

Therefore the final retardation  of an object will be

now from the formula we get

where s is the distance travelled in the liquid.

 Now the required time will be