Question: The ship is moving 50% of the speed of light, and Jim gets ejected. How did Jim have time to throw the door to change his trajectory? How did that throw outpace 50% of the speed of light?
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Answer: He didn't have to outpace that entire speed. Since he ejected from the ship, he was already moving the same speed as the ship. So throwing the door gave him a little bit of extra momentum on top of the speed he was already moving.
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