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# Please help with this SPECIAL RELATIVITY problem! DUE SOON! It has something to do with LENGTH, TIME, & SPEED. How fast does the ship move?

A spacecraft with a proper length of

400

m passes by an observer on the Earth. According to this observer, it takes

0.820

µ

s for the spacecraft to pass a fixed point. Determine the speed of the spacecraft as measured by the Earth-based observer.

__?__c

I have no clue why it did that weird spacing so here it is again.

A spacecraft with a proper length of 400 m passes by an observer on the Earth. According to this observer, it takes 0.820µs for the spacecraft to pass a fixed point. Determine the speed of the spacecraft as measured by the Earth-based observer.

__?__c

### 1 Answer

- Anonymous1 month ago
Lo = 4x10^2 m

t = 8.2x10^-5 s

L = Lo (1 - v^2 / c^2)^1/2

L = v t

then

v t = Lo (1 - v^2 / c^2)^1/2

v^2 t^2 = Lo^2 - (Lo^2 v^2) / c^2

Lo^2 v^2 + v^2 c^2 t^2 = Lo^2 c^2

v = [Lo / (Lo^2 + c^2 t^2)^1/2] c

v = [4x10^2 / (1.6x10^5 + 9x10^16*6.724x10^-11)1/2] c = 0.016 c = 4,81x10^6 m/s

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