You've been making mistakes. When you going to own up to it boss?
So how does your boy Felix land close to his launch point if the earth is rotating faster than the speed of sound?
Really. I want you to think about what you just asked.
The speed of anything is only relevant between two objects.
I'm sure you've witnessed the doppler effect of a train horn sometime in your life.
The speed of the soundwaves leave the horn at a fixed speed.
Then you have to add the speed of the train to the speed of the horn sound waves.
If the train is speeding towards you, the sound waves are coming at you faster than they are as the train goes away from you.
That's why the sound shifts as it goes by.
Felix's speed and the earth's surface speed are relevant to each other. If the earth's surface speed was zero, as you think, or if the earth's surface speed is about 1000mph at the equator as the rest of the world believes, the effects would be exactly the same.
We've already proven this concept to you in the example of jumping inside of a moving vehicle.
You know all of these examples can be observed and performed by yourself.