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A ballistic cart is a cart that can shoot a ball vertically and (maybe) catch it again.
With the cart rolling at constant speed when it shoots the ball, where will the ball land?
Both the ball and the cart have the same x-position at all times, so the ball must land back in the cart. The ball's x-velocity is not affected by its motion in the y direction.
If the cart is released from rest and accelerates down an incline, releasing the ball on the way down, where will the ball land?
If the cart is pushed up the incline, releasing the ball on the way up, where will the ball land?