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Kicking a football to fly
Here's a crazy idea:
Imagine that you kicked a football upwards. Then you jump upwards as high as you can. You time it so perfectly that as you begin to fall, the ball bounces back up to your leg. Now, you hit the ball as hard as you can, straight downward with perfect precision, so that you use the reaction force to
Kick a football up
Jump
Kick Down
Fly
Repeat by energy transfer