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•• Consider the relativistic snake of Example 1.6, but let the numbers be as follows: The snake has speed 0.6c and proper length of 100 cm (as before), but the boy holds the two hatchets 80 cm apart. (a) Show that with these lengths the experiment can be seen as a test of relativity, since the snake will be unhurt if relativity is right (and the boy times things correctly), whereas the snake will definitely be hurt if the classical ideas of space and time are correct. (Naturally, relativity is correct and the snake is unharmed.) (b) Use the Lorentz transformation to find the positions and times of the falling of the two hatchets as measured by the snake, and use these to verify that it is unharmed. (Assume the boy bounces the hatchets at t = 0, at which time the snake’s tail is at the common origin.)
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