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If you're falling down, but there isn't a wall on both sides (compare: no wall on the right side in this case), then the shadow gives the solution. When you release the rope, press space twice. This will cause you to shoot the rope and immediately release it, changing the direction you shoot the rope.
Using the shadow also make you fall a bit faster at the start, so it could be used to win time. Sometimes though, it seems to slow you down instead of speed you up. You'll have to find out for yourself when to use it and when not to.
Using the shadow for a slightly different occasion