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Consider Alice’s spaceship with the paintball apparatus that shoots two paintballs toward clocks at opposite ends of her ship, each with speed S relative to the apparatus (similar to the video lecture). Assume that Alice has properly synchronized her clocks, that her spaceship is moving with speed V to the right (in the positive x direction) relative to Bob, that S is greater than V, and that S and V are much less than the speed of light. According to Bob’s observation of Alice’s spaceship (and clocks and paintballs) flying by, what will be the speed of the paintball that is moving to the left? (In other words, what is the speed in Bob’s frame of reference? We’re interested in the speed as the magnitude of velocity, so don’t worry about whether it might be positive or negative.)
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