A yet-to-be-built spacecraft starts from Earth moving at constant speed to the yet-tobe-discovered planet Retah, which is 20 lighthours away

Question

A yet-to-be-built spacecraft starts from Earth moving at constant speed to the yet-tobe-discovered planet Retah, which is 20 lighthours away from Earth. It takes 25 h (according to an Earth observer) for a spacecraft to reach this planet. Assuming that the clocks are synchronized at the beginning of the journey, compare the time elapsed in the spacecraft’s frame for this one-way journey with the time elapsed as measured by an Earth-based clock.

in progress 0
Orla Orla 5 years 2021-08-28T15:41:41+00:00 1 Answers 33 views 0

Answers ( )

  1. trucchi
    0
    2021-08-28T15:42:47+00:00
    Reply

    Answer:

    The  time elapsed at the spacecraft’s frame is less that the time elapsed at earth’s  frame

    Explanation:

    From the question we are told that

    The distance between earth and Retah is  d = 20 \ light \ hours = 20 * 3600 * c = 72000c \ m

    Here c is the peed of light with value c = 3.0*10^8 m/s

    The time taken to reach Retah from earth is  t = 25 \ hours = 25 * 3600 =90000 \ sec

    The velocity of the spacecraft is mathematically evaluated  as

         v_s = \frac{d }{t}

    substituting values

       v_s = \frac{72000 * 3.0*10^{8} }{90000}

        v_s = 2.40*10^{8} \ m/s

    The time elapsed in the spacecraft’s frame is mathematically evaluated as

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

    substituting value

           T = 90000 * \sqrt{ 1 - \frac{[2.4*10^{8}]^2}{[3.0*10^{8}]^2} }

            T = 54000 \ s

    =>    T = 15 \ hours

    So  The  time elapsed at the spacecraft’s frame is less that the time elapsed at earth’s  frame

           

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )