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Speed of Light and Galileo

  1. Feb 26, 2006 #1
    I'm having trouble with a proble I'm trying to complete. The Problem states:

    Galileo attempted to measure the speed of light by measuring the time elapsed between his opening a lantern and his seeing the light return from his assistant's lantern. The experiment is illustrated in Figure 25-24. What distance, d, must separate Galileo and his assistant in order for the human reaction time, t = 0.2 s, to introduce no more than a 18% error in the speed of light?

    The only way I can think to do the problem is with, time = distance/speed of light. Time would equal 0.1 s and speed of light minus 18% error (I think its minus, because the error would make the velocity seem slower) would be 2.46E8 m/s. d= 0.1s(2.46E8 m/s) = 2.46E7 m (the wrong answer). Any suggestions? Thanks
  2. jcsd
  3. Feb 27, 2006 #2

    Andrew Mason

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    The measured speed would be [itex]c_{m} = d/t[/itex] where t = total elapsed time which includes the reaction time of .2 sec.

    The actual speed of the light would be [itex]c = d/(t-t_r)[/itex]

    So the question asks: what value of d will make the difference [itex]c-c_m[/itex] less than or equal to .18c? That means that [itex]c_m \ge .82c [/itex].

    Use the relationship: [itex]t - t_r = d/c[/itex] and [itex]t = d/c + t_r[/itex]

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