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 the figure(Figure 1). You may want to review (Pages 885 - 889) .
PART A: What distance, d, must separate Galileo and his assistant in order for the human reaction time, Δt = 0.2 s, to introduce no more than a 11 % error in the speed of light?
With steps please, thanks.
Time, t = 2d/c ...... (1)
(1 - 0.11)c = 2d/(t + dt)
0.89c = 2d/(t + dt)
From equation (1),
0.89c = 2d/[(2d/c) + dt]
2d + c dt = 2dc/0.89c
d = - c dt/[2(1 - 1/0.88)]
d = - (3 x 10^8 x 0.2)/(-0.27)
d = 2.2 x 10^8 m
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Galileo attempted to measure the speed of light by measuring the time elapsed between his opening...