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

A snake of proper length 100 cm is moving at speed v = 0.6c to the right across the table. A mischievous boy, wishing to tease the snake, holds two hatchets 100 cm apart and plans to bounce them simultaneously on the table so that the left hatchet lands immediately 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. This implies that the right hatchet will fall 20 cm in front of the snake, and the snake will be unharmed”. On the other hand, the snake argues “the hatchets are approaching me at 0.6c, and the distance between them is 80 cm. Since I am 100 cm long, I will be cut in pieces when they fall” (it’s a very smart snake).

Use Lorentz transformation to resolve this apparent paradox. In other words, resolve it quantitatively, not just with a qualitative argument about non-simultaneity.

Please show work quantitatively, thanks!

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Expert Solution

genius_generous answered 1 year ago

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