Kinetic energy is given by the formula:
\[ KE = \frac{1}{2}mv^2 \]
where \(KE\) is the kinetic energy, \(m\) is the mass of the object, and \(v\) is its velocity.
In your scenario, Object 1 is dropped first and starts gaining speed as it moves down the hill. By the time Object 2 is dropped (when Object 1 is halfway down the hill), Object 1 will have a certain velocity and therefore a certain kinetic energy.
When you drop Object 2 at that point, it starts from rest and will begin to accelerate down the hill, but it will not have any kinetic energy initially (since its velocity is zero at the moment it is dropped).
As Object 1 continues to move down the hill, it will keep gaining speed and thus will increase its kinetic energy. By the time Object 2 reaches the same point as where Object 1 was dropped, Object 1 will have already accumulated more kinetic energy than Object 2 will have, since Object 2 started from rest and has not had as much time to accelerate.
Therefore, at any moment after the drop, Object 1 will have the highest kinetic energy compared to Object 2, assuming they are subject to the same gravitational forces and conditions (i.e., ignoring air resistance).