If a 1150 kg artillery shell is fired from a 165000 kg battleship with an acceleration of 16.9 m/s216.9~\text{m/s}^216.9 m/s2, then what is the recoil acceleration of the ship? (for this calculation, neglect the force of the water on the ship)

For Newton's third law, for every action there is an equal and opposite reaction. This means that the force the battleship exerts on the artillery shell is equal (and opposite) to the force exerted by the shell on the battleship. Since the force is the product between the mass and the acceleration, the previous statement becomes, in formula:

where the term on the left is the force exerted on the shell and the term on the right is the force exerted on the battleship, and where
is the mass of the shell
is its acceleration
is the mass of the battleship
is its acceleration

By re-arranging this equation and by using the data of the problem, we can calculate , the recoil acceleration of the battleship: