The bullet leaves the cart vertically and this very moment its horizontal component of speed is equal to the horizontal component of the cart. In the fixed coordinates, the bulled trajectory will be parabolic, and relatively to the cart the bulled will go up and fall down exactly the same hole it left. So, the bullet will go back giving the same impulse to the cart as it was a period of time ago. Thus the profile of cart’s speed should have two identical ramps separated by a period of time.