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Galileo’s Descendent

Galileo is purported to have tried to measure the speed of light by having two men climb 2 different hills, and flash lantern lights back in force, and measure the lapse in time, discounting for human reaction time. Of course, even if he had performed this experiment, it would not have worked, given that the speed of light is so fast that it can travel around the earth seven times in one second. However, Braggadocio, a great, great, great, great nephew of the honored Galileo, living in present-day New England, being somewhat arrogant, thinks he is smarter than his great, great, great, great uncle, and he can successfully perform the experiment because he has such quick reflexes.
Instead of using two nearby hills, Braggadocio decides to use the top of Mount Katahdin, 1 mile high (actually, it lacks 13 feet of being one-mile, but close enough for our purposes), at the northern terminus of the Appalachian Trail in Maine. He intends to flash the light from Mount Washington across the border in New Hampshire, 150 miles away, but realizes that numerous peaks of the Appalachian Mountains obscure the view in between, so he decides to set up somewhat eastward on Pleasant Mountain in Maine, not as high, at only a little over a third (.367) of a mile altitude, but also 150 miles away and without intervening mountains.
He waits for a perfectly clear night, uses powerful lamps that can be seen clearly over that distance, and sends his cousin, Pinocchio, whose reflexes are equally as fast as Braggadocio's, to the top of Mount Katahdin. The experiment fails, but not because the speed of light is too fast to measure. (Braggadocio still claims that he is fast enough to do it.) Why does the experiment fail?
(Hint: It is not because I did not use enough "great greats" in the preceding description!)

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