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Satellites are visible and move at some km per second. Pretty fast
Inside the atmosphere anything faster than some hundreds km/h get so much drag that they either are extremely small (bullets) or extremely powerful (planes, maglev trains)
And planes reach their higher speeds only at altitude where density is lower
Are we observing them moving, or are they stationary and we are the ones moving? dramatic dun-dun-duuuunnnn
(kinda joke kinda serious)
The answer is yes, depending on your frame of reference.
Everything in the Universe is moving.
You're moving at about 700 m/s while sitting in your couch, according to Earth's rotation. So if the plane goes west at max speed, it would be 1400 m/s faster than going east.