Step-by-step explanation:
When the mallet hits the ball with an action force, the ball exerts a reaction force on the mallet, as explained by newton's third law of motion
According to Newton's third law of motion, action and reaction are equal and opposite.
The ball starts to move when the mallet applies a net force to it, as explained by newton's "second law of motion"
According to newton's second law of motion "the net force on a body is the product of mass and acceleration of the resultant of forces"
Once a ball is hit and no longer touches the mallet, it continues moving because of its inertia, as explained by netwon's first law of motion;
"according to the first law, body will continue in its state of rest or of uniform motion unless if it is acted upon by an external force". The law is also known as the law of inertia.