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attashe74 [19]
3 years ago
13

You have been posted to a remote region of space to monitor traffic. Near the end of a quiet shift, a spacecraft streaks past. Y

our laser-based measuring device reports the spacecraft’s length to be 85 m. The identification transponder reports it to be the NCXXB12, a cargo craft of proper length 100 m. In transmitting your report to headquarters, what speed should you give for this spacecraft?
Physics
1 answer:
natima [27]3 years ago
3 0

Answer:

The value is v =1.58 *10^{8} \  m/s

Explanation:

From the question we are told that

The length of the spacecraft streaks is L_i =  85 \  m

The proper length of the spacecraft streaks L_p  =  100 \  m

Generally from the equation of relativity of length contraction

L_i  =  L_p  *  \sqrt{1 - \frac{v^2}{c^2} }

Here c is the speed of light with value c =  3.0 *10^{8} \  m/s^2

v is the velocity of the spacecraft

So

\frac{v^2}{c^2}  =  1 - \frac{L_i^2}{L_p^2 }

=> \frac{v^2}{c^2}  =  \frac{L_p^2 - L_i^2}{L_p^2}

=> \frac{v^2}{c^2}  =  \frac{100^2 - 85^2}{100^2}

=> \frac{v^2}{c^2} =  0.2775

=>  v =  \sqrt{0.2775c^2}

=>  v = 0.5268c

=>  v = 0.5268 *  3.0*10^{8}

=>  v =1.58 *10^{8} \  m/s

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