Hello. I have a question about a problem from Morin's book, Introduction to classical Mechanics.(adsbygoogle = window.adsbygoogle || []).push({});

Problem 11.6. The problem and it's proposed solution are attached.

The condition for the (light-speed traveling) pulse to "win the race" with the bomb is, by the book,

[tex]

L/c < L(1-1/\gamma)/v

[/tex]

meaning that the travel time of the pulseto the front of the tunnelwould be less than the time of the bomb reaching the front.

But I thought the condition should be that the travel time of the pulseto the front of the trainwould be shorter than the bomb's. that is,

[tex]

\frac{L/\gamma}{c-v}< L(1-1/\gamma)/v

[/tex]

It appears to be leading to the same expression, but still, the condition is different.

Why is the proposed condition correct?

(it seems to me that it is enough for the pulse to get to the front of the train, even before the front of the train makes it to the end of the tunnel).

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