In kinematics, the x and y components of velocity are indeed independent of each other in the absence of external forces. This means that changes in the x-component of velocity do not affect the y-component of velocity and vice versa. However, when an object is subject to the force of gravity, the situation becomes different.
When studying orbits, such as the motion of a satellite around the Earth, the gravitational force plays a crucial role. The force of gravity acts as a centripetal force, continuously pulling the satellite toward the center of the Earth and causing it to move in a curved path.
If the velocity in the x-direction (horizontal direction) is large enough, it can counteract the gravitational pull and prevent the satellite from hitting the Earth. This is because the gravitational force acts vertically downward, while the object's velocity is horizontally oriented. As long as the horizontal component of the velocity is sufficient to balance the gravitational force, the object will remain in orbit and continue to revolve around the Earth.
In other words, the combination of the object's horizontal velocity and the gravitational force determines the shape and stability of the orbit. If the horizontal velocity is too low, the gravitational force will overpower it, causing the object to fall back to Earth. On the other hand, if the horizontal velocity is too high, the object will escape the gravitational pull and move away from the Earth.
It's important to note that the x and y components of velocity remain independent in the sense that changes in one component do not directly affect the other component. However, in the case of objects in orbit, the interplay between the gravitational force and the object's velocity results in a coordinated motion that allows the object to stay in a stable orbit around the Earth.