Please Help!!!! Your Best friend gets on a ship and travels away fast. They return 10.0 years later and I’ve only aged 4.00 yea

Question

Please Help!!!!

Your Best friend gets on a ship and travels away fast. They return 10.0 years later and I’ve only aged 4.00 years. How fast was your friend traveling? Give your answer as ex. 0.5c

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Sapo 2 months 2021-07-30T04:51:44+00:00 1 Answers 2 views 0

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    2021-07-30T04:53:09+00:00

    Answer:

    v = 0.92 c

    Explanation:

    Here, we will use the time dilation formula from Einstein’s theory of relativity to find the speed of traveling of the friend:

    t =\frac{t_o}{\sqrt{1-\frac{v^2}{c^2}}} \\\\\\\sqrt{1-\frac{v^2}{c^2}}=\frac{t_o}{t}\\\\

    where,

    v = speed of traveling = ?

    c = speed of light

    t = time of return = 10 years

    t₀ = time passed on earth = 4 years

    Therefore,

    \sqrt{1-\frac{v^2}{c^2}} = \frac{4\ years}{10\ years}\\\\  1-\frac{v^2}{c^2}=(\frac{2}{5})^2\\\\\frac{v^2}{c^2} = 1-\frac{4}{25}\\\\\frac{v^2}{c^2} = \frac{21}{25}\\\\v^2 = 0.84c^2\\\\

    v = 0.92 c

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