Final answer:
The ball fired straight up from a cart rolling at constant velocity will land directly in the tube, because it maintains the same horizontal motion as the cart while in flight.
Step-by-step explanation:
If a cart that is rolling at a constant velocity on a level table fires a ball straight up, the ball will land directly in the tube assuming there is no air resistance and no horizontal forces acting on the ball after it is launched. This is because the ball will have the same horizontal velocity as the cart at the moment of launch. During the ball's flight, both the ball and the cart will move horizontally at the same rate. When considering projectile motion and X-Y independence, the ball's horizontal velocity remains constant while the vertical motion is affected by gravity alone. At the ball's highest point, its vertical velocity is zero, but the horizontal velocity is unchanged. It's important to note that the acceleration due to gravity acts downward throughout the flight, but this does not affect horizontal motion.