Observer \(S\) is at rest on the ground in an inertial reference frame. Observer \(S'\) is inside a vehicle that travels along a straight, horizontal track with a constant acceleration of magnitude \(a_0\) directed to the right relative to the ground. At \(t = 0\), a small object is dropped from rest relative to Observer \(S\) and falls vertically with negligible air resistance. Which of the following statements correctly describes the horizontal component of the object's acceleration as measured by Observer \(S'\) and provides the correct justification?