Three clay balls are sliding on a horizontal, frictionless surface toward the origin as shown in the figure. Ball 1 has mass \(m\) and is moving with speed \(v\) in the \(+x\)-direction. Ball 2 has mass \(2m\) and is initially at rest at the origin. Ball 3 has mass \(2m\) and is moving with speed \(v\) in the \(+y\)-direction. The three balls collide simultaneously at the origin and stick together to form a single combined object. Which of the following correctly describes the \(x\)-component of the velocity of the combined object after the collision and provides a valid justification?