Final answer:
According to Newton's third law, the horse and cart move forward because of the equal and opposite reaction forces between them. When the horse pushes backward, the ground pushes forward, propelling the horse and cart forward. Similarly, when the cart pulls back, the horse pushes forward, allowing the horse and cart to move forward.
Step-by-step explanation:
Newton's third law states that for every action, there is an equal and opposite reaction. In the case of the horse and cart, when the horse moves forward, it exerts a force on the ground in the backward direction. According to Newton's third law, the ground exerts an equal and opposite reaction force on the horse in the forward direction. This reaction force propels the horse and cart forward.
Similarly, when the cart pulls back with the same force but in the opposite direction, it exerts a force on the horse in the forward direction. Again, according to Newton's third law, the horse exerts an equal and opposite reaction force on the cart in the backward direction. These forces cancel each other out, allowing the horse and cart to move forward instead of remaining at rest.