The principle of conservation of linear momentum states that if in any assigned direction the net external force on a system is zero, then the linear momentum of the system will remain constant in that direction. Answer the following question.
Suppose the mass of the cart along with your mass is 100 kg and there are 4 balls each of mass 2 kg in the cart that is now moving at a constant speed 20 ms to the left on the frictionless track. If you throw a ball straight up with a velocity 20 ms, how will the speed of the cart change?
The speed of the cart will not change
Since the ball is thrown perpendicular to the motion of cart, it has no effect on the cart. While in the air, the ball will maintain its motion due to inertia in the left-hand direction. The force that is acting on the system is an internal force. Hence, there exists no external force in the horizontal direction that can change the speed of the cart. Thereby, there will be no change in the speed of the cart.