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A snake of proper length 100 cm is moving at speed v = 0.6c to the...

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Physics

A snake of proper length 100 cm is moving at speed v = 0.6c tothe right across the table. A mischievous boy, wishing to tease thesnake, holds two hatchets 100 cm apart and plans to bounce themsimultaneously on the table so that the left hatchet landsimmediately behind the snake’s tail 1 .

The boy argues as follows: “The snake is moving with v = 0.6c,therefore, its length measured in my frame is 100cm γ = 80 cm. Thisimplies that the right hatchet will fall 20 cm in front of thesnake, and the snake will be unharmed”. On the other hand, thesnake argues “the hatchets are approaching me at 0.6c, and thedistance between them is 80 cm. Since I am 100 cm long, I will becut in pieces when they fall” (it’s a very smart snake).

Use Lorentz transformation to resolve this apparent paradox. Inother words, resolve it quantitatively, not just with a qualitativeargument about non-simultaneity.

Please show work quantitatively, thanks!

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