(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Anna is on a railroad flatcar moving at 0.6c relative to Bob. Her arm is outstretched in the dirction the flatcar moves, and in her hand is a flashbulb. According to her wristwatch, the bulb goes off at 100 ns. This even according to Bob differs by 27 ns.

a) is it earlier or later than 100 ns?

b) how long is Anna's arm?

2. Relevant equations

lambda_{v}= 1 / sqrt[(1-v^{2}) / c^{2}]

3. The attempt at a solution

a) I'm a little bit confused by time dilation. I think that since Anna is moving according to Bob's frame of reference, he sees a longer time interval for her. Therfore, his watch would read later than 100 ns. I think?

b)lambda_{v}= 1 / sqrt[(1-v^{2}) / c^{2}]

= sqrt(1-0.6^{2})

=1.25

I'm confused about where to go from here. I need the length of Anna's arm. I know that this is the length from her hand to her center of mass. So if she is moving at 0.6c relative to Bob, and he sees the light go off at 127 ns,

d = vt

= 0.6c(127)

=76.2 cm

L_{0}= L x lambda_{v}

= 76.2 x 1.25

= 95.25 cm

So I found the length of her arm to be 95 cm. However, I have a feeling this isn't correct. I'm not sure I used the right formula...

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# Time dilation and length contraction problem

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