Question

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)

Answer 1

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:

`m_s a_s = M_b a_b`
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

`m_s` is the mass of the shell

`a_s` is its acceleration

`M_b` is the mass of the battleship

`a_b` is its acceleration

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

`a_b = (m_s a_s)/(M_b)= ((1150 kg)(16.9 m/s^2))/(165000 kg)=0.118 m/s^2`