According to Newton's Third Law, a force in one direction produces an equal force in the opposite direction. If the force that acts on a cannonball and the recoiling cannon are equal in magnitude, why does the cannon not recoil with the same velocity at the cannonball?
Yes, the forces are the same. Now we assume there is no resistance from the air and the ground. So that force is the only force. Then accroding to Newton's second law
where m_ball, and m_cannon are the ...
The solution explains the reason why the cannon does not recoil at the same velocity as the cannonball from two different prospective, Newton's third law and conservation of momentum.