Final answer:
The horizontal component of the rock's velocity remains constant as it rises toward its apex if air resistance is negligible, due to the absence of any external horizontal forces.
Step-by-step explanation:
When a rock is thrown upward at 50 degrees with respect to the horizontal, and air resistance is negligible, the horizontal component of the rock’s velocity remains constant as it rises toward its apex. This is due to Newton's first law of motion, which states that an object in motion will stay in motion with a constant velocity unless acted upon by an external force. In the absence of air resistance, there is no external horizontal force to change the horizontal velocity of the rock.
So, the correct answer to the question is: A) Remains constant.
If air resistance were not negligible, it could affect both the speed of the rock upon its return to the starting point and the maximum height it reaches by slowing the rock down, but since the question specifies that air resistance is negligible, these factors do not apply in this scenario.