An intergalactic rock star bangs his drum every 1.30 s. A person on earth measures that the time between beats is 2.50 s. How fast is the ro

Question

An intergalactic rock star bangs his drum every 1.30 s. A person on earth measures that the time between beats is 2.50 s. How fast is the rock star moving relative to the earth

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Khang Minh 3 years 2021-08-08T00:39:18+00:00 1 Answers 13 views 0

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  1. thienan
    0
    2021-08-08T00:41:13+00:00
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    Answer:

    v = 0.89 c = 2.67 x 10⁸ m/s

    Explanation:

    The time dilation consequence of the special theory of relativity shall be used here, From time dilation formula we have:

    t = t₀/√[1 – v²/c²]

    where,

    t = time measured by the person on earth = 2.50 s

    t₀ = rest time of the intergalactic rock star = 1.30 s

    v = relative speed of the rock star = ?

    Therefore,

    2.5 s = (1.3 s)/√[1 – v²/c²]

    √[1 – v²/c²] = 1.3/2.5

    √[1 – v²/c²] = 0.52

    [1 – v²/c²] = 0.52²

    [1 – v²/c²] = 0.2074

    v²/c² = 1 – 0.2074

    v²/c² = 0.7926

    v/c = √0.7926

    v = 0.89 c

    where,

    c = speed of light = 3 x 10⁸ m/s

    v = (0.89)(3 x 10⁸ m/s)

    v = 0.89 c = 2.67 x 10⁸ m/s

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