Final answer:
The cart on the frictionless track will indeed be put into motion towards the right when a ball is thrown to the left due to Newton's third law of motion.
Step-by-step explanation:
If you throw a ball off the cart towards the left while on a frictionless track, the cart will be put into motion towards the right. This is due to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. As you throw the ball to the left, the ball exerts an equal force onto you and the cart to the right. No external forces are acting on the cart, so according to Newton's first law of motion, the cart was initially at rest and stays in a state of rest until an external force acts upon it. In this scenario, the only force acting is between the ball and the cart during the throw, which causes the cart to move in the opposite direction of the throw.