Law of Action/Reaction
Newton’s thirds law states that for every force, there is an equal and opposite reaction force. This occurs during contact between the racquet and the ball. Yes, the racquet applies a force to the ball, but that is not what moves the ball. The force that moves the ball is actually the force of the ball pushing back against the strings of the racquet. When the ball is hit, it is compressed briefly, and then it retakes it original shape, pushing back on the strings. Had the ball not pushed back, the strings would have just compressed the ball, and the ball would have stayed on the strings, but since the ball pushed back once it had been compressed, it bounced off the stings and was sent into the air. The fact that the ball moves shows us that this law is occurring. If the ball had not moved, it would have been proof that there was no reaction force reacting to the racquet hitting the ball, but it did move, so we know there was a reaction force.