A radar antenna is rotating and makes one revolution every 24 s, as measured on earth. However, instruments on a spaceship moving with respe

Question

A radar antenna is rotating and makes one revolution every 24 s, as measured on earth. However, instruments on a spaceship moving with respect to the earth at a speed v measure that the antenna makes one revolution every 44 s. What is the ratio v/c of the speed v to the speed c of light in a vacuum

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Adela 5 years 2021-08-29T05:14:24+00:00 1 Answers 54 views 0

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  1. mit
    0
    2021-08-29T05:15:38+00:00
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    Answer:

    0.838

    Explanation:

    The ratio v/c of the speed v to the speed c of light in a vacuum is shown below:

    Given that

    \triangle t_0 = 24\ seconds = time interval for one revolution

    \triangle t = 44\ seconds = time interval measured with speed v

    based on the given information, the ratio v/c  of the speed v to the speed c of light in a vacuum is

    \triangle t = \frac{\triangle t_0}{\sqrt{1 - \frac{v^2}{c^2}}}

    {\sqrt{1 - \frac{v^2}{c^2}}} = \frac{\triangle t_0}{\triangle t}

    Now squaring both the sides

    \frac{v^2}{c^2} = 1 - \frac{(\triangle t_0)^2}{(\triangle t)^2}

    Now remove the squaring root from both the sides and putting the values

    \frac{v}{c} = {\sqrt{1 - \frac{(\triangle t_0)^2}{(\triangle t)^2}

    = {\sqrt{1 - \frac{(24)^2}{(44)^2}

    = 0.838

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