When an airplane is flying in the opposite direction of the Earth's rotation, it does not necessarily fly faster in relation to the ground. The speed of an airplane is typically measured relative to the air mass through which it is moving, rather than the ground below.
In terms of groundspeed, which is the speed of the aircraft relative to the Earth's surface, various factors come into play. The primary factor is the speed of the aircraft relative to the air mass, known as the airspeed. The Earth's rotation does affect the groundspeed but not directly.
If an airplane is flying directly into a headwind (opposite to the direction of the Earth's rotation), the groundspeed will be reduced. It may seem as if the airplane is flying slower because it takes more time to cover the same distance over the ground. However, the airspeed remains the same; it is the speed of the wind relative to the airplane that affects the groundspeed.
On the other hand, if the airplane is flying with a tailwind (in the same direction as the Earth's rotation), the groundspeed will be increased. It may appear as if the airplane is flying faster because it takes less time to cover the same distance over the ground. Again, the airspeed remains the same, but the speed of the wind adds to the groundspeed.
So, when flying in the opposite direction of the Earth's rotation, the airplane's groundspeed may be lower if there is a headwind, but it does not necessarily mean that the airplane is flying faster in terms of airspeed.