From Googling:
How far can you see a boat before it disappears because of the curvature of the Earth?
Assuming a man's height to be about 6 feet, that is, 1.8 meters and earth's radius is 6400,000 meters. Assuming earth is spherical.
The right triangle formed is :
View attachment 672650
The right triangle formed is :
And we have equation
(R+x)^2 = R^2 + y^2
R and x are known (see above), and y is to be known.
Calculation tells y is little more than 5 Kms.
Next, y should be approximately equal to the distance of the boat from the feet of man. Thus, he will be able to see the boat up to little more than 5 Kms.
How far away can gunshots be heard from?
It would depend on the gun as some are louder than others but essentially two miles before no one could hear it. The dB drops pretty fast for instance a rifle of 134 decibels at the gun would most likely not be recognizable at two miles.
Two is less than 5, although other factors could mitigate. Can we be done now? I know, I said I was done before, but I hate to concede and I thought others might pick up the discussion.
PS: I believe the lights were on.
