If you were to stand at the edge of a spinning Earth and throw something straight up, several factors would come into play:
Inertia: The object you throw retains its initial velocity in the same direction as Earth's rotation. This means that it would continue to move eastward, parallel to the Earth's surface, at the same speed as the point from which it was thrown.
Earth's Rotation: As the object moves upward, Earth continues to rotate beneath it. From your perspective on the ground, it might appear as though the object is curving to the east due to the rotational motion of the Earth. However, in reality, the object maintains a straight-line trajectory with respect to space.
Gravitational Pull: Gravity acts on the object, pulling it back towards the Earth. As the object moves higher, the gravitational force decreases due to the inverse square law. This means that the acceleration due to gravity decreases with distance, resulting in a gradually weaker downward pull.
As a result of these factors, the object would follow a curved path relative to an observer on the rotating Earth. It would initially move upward and eastward but gradually slow down due to the gravitational force pulling it downward. Eventually, if the initial velocity is not sufficient to overcome the pull of gravity, the object would reach its highest point and then fall back towards the Earth in a parabolic or elliptical trajectory, depending on the specific initial conditions.
It's important to note that these effects become more apparent for objects with longer flight times, such as rockets or satellites, as the Earth's rotation has more time to influence their paths. For short durations or low speeds, the influence of Earth's rotation on the trajectory of the object may be negligible.