How Did Galileo's Lantern Experiment Attempt to Measure the Speed of Light?

[Flyfishinva]

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

 

[Andrew Mason]

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

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

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

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

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

AM