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(B) Consider the rail car and the sand as a single system. The external forces acting on this system in the horizontal direction are zero because the

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The car maintains the same speed

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(B) Consider the rail car and the sand as a single system. The external forces acting on this system in the horizontal direction are zero because the track is frictionless and the sand is falling vertically.According to the principle of conservation of linear momentum,the total momentum of the system must remain constant.The momentum of the system is given by $P = Mv$,where $M$ is the total mass of the car and the sand,and $v$ is the velocity of the car.As the sand pours out vertically,it carries no horizontal momentum relative to the car. Since the sand is falling straight down,its horizontal velocity component remains equal to the horizontal velocity of the car at the moment it leaves the car.Because there is no external horizontal force acting on the system,the horizontal velocity of the car does not change.Therefore,the speed of the rail car remains $v_0$.

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