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« on: January 14, 2016, 09:42:19 PM »
Short answer:
1. Yes, kind of.
2. Relativity
3. Relativity
4. Relativity
Long answer:
1. Planes constantly makes adjustments to the direction the plane is facing in order to maintain a constant altitude. A plane flying completely straight with no adjustments would indeed find itself climbing in altitude, but compared to the effect things like a moderate breeze might have on the altitude of the plane, the curvature of the Earth is simply not dramatic enough to have a significant impact on the altitude of the plane. It gets washed out by larger effects which require adjustments to maintain a constant altitude.
2. The plane sitting on the surface of the Earth has a certain inertia associated with it, due to the spinning of the planet. If you were for example to take a balloon up into the sky, you'd be moving at the same relative speed as the surface below you, so you can't just wait for your destination to slide underneath you.
3. Again, this is just another point about relativistic motion. If we were to take the center of the Earth as a reference frame, you would indeed be moving faster while traveling in one direction versus the other. The problem arises when you consider that the surface is also moving faster relative to the center, so that you have to be moving faster (relative to the center of the Earth) to "catch up" with the surface as it rotates.
4. Once again, relativity. You can land on a north facing runway because both you and the runway are moving at a relative speed of 1000 mph in the same direction (relative to the center of the Earth). As a result, it appears that the runway isn't moving at all. Imagine two boats side by side on the ocean, moving at the same speed to each other. It's not difficult at all for me to take a step perpendicular to their motion from one boat to another, because we're all moving at the same relative speed. The same case applies to the airplane.