No, it is not possible for a plane to outrun the rotation of the Earth. The Earth rotates at a speed of approximately 1670 kilometers per hour (1040 miles per hour) at the equator. This rotational speed is much greater than the maximum speed of any aircraft currently in operation. The fastest commercial jet airliners can reach speeds of around 900 to 1,000 kilometers per hour (560 to 620 miles per hour), while military fighter jets can achieve speeds of up to Mach 2 (twice the speed of sound).
Even if an aircraft were able to achieve a speed close to the Earth's rotational speed, it would still be moving relative to the Earth's surface and would experience the same rotational effects as any other object on the planet. The rotation of the Earth affects everything on its surface, including the atmosphere and the air currents within it. The airplane would still be subject to the same prevailing winds and atmospheric conditions that exist due to the Earth's rotation.
Moreover, even if it were somehow possible for an aircraft to achieve a speed faster than the Earth's rotation, it would face numerous practical challenges. The enormous fuel consumption required to maintain such a speed for an extended period would be highly impractical and unsustainable. Additionally, the tremendous forces and stresses on the aircraft and its structure at such high speeds would likely pose significant safety risks.
In summary, while aircraft can travel at high speeds, they cannot outrun the rotation of the Earth due to the vast difference in speed and the physical limitations involved.