(Solved): include a free body diagram in the process please  A test projectile is fired horizontally into ...

A test projectile is fired horizontally into a viscous liquid with a velocity \( 100 \mathrm{~m} / \mathrm{s} \). The retarding force is proportional to the square of the velocity, so that the acceleration becomes \( a=-0.8 v^{2} \). Derive expressions for the distance \( D \) traveled in the liquid and the corresponding time \( t \) required to reduce the velocity to \( 50 \mathrm{~m} / \mathrm{s} \). Neglect any vertical motion. \{0.66 \( \mathrm{m}, 0.0125 \mathrm{~s}\} \)