If you were standing at the edge of a spinning Earth and threw something straight up, the object would initially continue to move in the same direction as the Earth's rotation. This is due to the principle of inertia, which states that an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an external force.
So, if you threw the object straight up, it would inherit the linear velocity of your hand due to your initial throw, which matches the rotational speed of the Earth at your location. As a result, the object would continue moving eastward (in the same direction as the Earth's rotation) while also moving vertically upward.
However, as the object moves higher into the atmosphere, it would be subject to the influence of other forces, such as gravity and air resistance. Gravity would gradually slow down the object's vertical motion, eventually bringing it to a stop. At that point, the object would begin to fall back down towards the Earth due to the gravitational force acting on it.
When the object descends, it would still retain the eastward velocity it acquired from the Earth's rotation initially. Therefore, the object would appear to curve eastward from its initial position as it falls back towards the ground.
In summary, the object would move in a curved path, combining the initial eastward velocity due to the Earth's rotation with the downward pull of gravity.