This question is related to the references you choose. This question is well-founded.

First, the moon rotates on its own, so although it is vertical when it is launched, it will fly obliquely upward along a parabolic trajectory. People on the surface of the moon move at the same speed as rockets in the horizontal direction, so they will see rockets rise vertically to the surface of the moon.

Second, this is the same principle as dropping bombs on airplanes. From the plane, the dropped bomb fell vertically to the ground, but what people on the ground saw was that the bomb fell along the curve of parabola.

Third, the condition of uniform linear motion gives you the balance of two forces. The condition of the balance of two forces is that the object is moving in a straight line at a uniform speed or at rest, so it can be used as a static object for force analysis. If an object leaves the ground, its direction of motion must be opposite and vertical. Therefore, in this problem, only when the resultant force is zero can the object move in a straight line at a uniform speed.