Suppose you went to the beach and you shoot a laser beam over the ocean, perfectly horizontal. The beam starts at sea-level, exactly.
How far above the ocean surface will the laser beam be at a distance of 8 km?
To answer this question, we need to consider the curvature of the Earth. The Earth is not flat, so as the laser beam travels over a distance, it will gradually curve downwards due to the Earth's curvature.
To calculate how far above the ocean surface the laser beam will be at a distance of 8 km, we can use the formula for the Earth's curvature:
h = R - sqrt(R^2 - d^2)
Where:
- h is the height above the sea level that we want to find,
- R is the radius of the Earth, which is approximately 6,371 km,
- and d is the horizontal distance from the starting point of the laser beam.
Let's plug in the values into the formula:
h = 6,371 km - sqrt((6,371 km)^2 - (8 km)^2)
Calculating this equation, we get:
h ≈ 4.91 meters
Therefore, at a distance of 8 km, the laser beam will be approximately 4.91 meters above the ocean surface.