A person is standing at the edge of the water and looking out at the ocean. The height of the person's eyes above the water is h = 1.6m. and the radius of the earth is R = 6.38 X 10^6 m. (a) How far is it to the horizon?
9.7
To determine the distance to the horizon, we can use the formula for the distance to the horizon on a perfect sphere:
d = √(2Rh + h²)
Where:
d = distance to the horizon
R = radius of the Earth
h = height of the person's eyes above the water
Plugging in the given values, we have:
d = √(2 * (6.38 X 10^6) * 1.6 + 1.6²)
Let's simplify the equation step by step:
d = √(2 * (10208000) + 2.56)
= √(20416000 + 2.56)
= √20416002.56
Now, we can find the square root using a calculator. The result will give us the distance to the horizon from the person's viewpoint.