The Earth has a radius of about 6.38 ´ 103 kilometers at the equator and rotates 360° every 24 hours. The angular displacement of a person standing at the equator for 8.0 hours is:

To find the angular displacement of a person standing at the equator for 8.0 hours, we can use the formula:

Angular Displacement = (Arc Length) / (Radius)

First, we need to calculate the arc length. Since the Earth rotates 360° every 24 hours, we can find the fraction of the rotation corresponding to 8.0 hours:

Fraction of Rotation = (8.0 hours) / (24 hours) = 1/3

Now, we can find the arc length:

Arc Length = (Fraction of Rotation) * (Circumference of Earth)

The circumference of a circle is given by the formula:

Circumference = 2 * π * Radius

Given that the radius of the Earth at the equator is about 6.38 × 10^3 kilometers:

Circumference = 2 * π * (6.38 × 10^3 kilometers)

Now, we can substitute this value into the equation for Arc Length:

Arc Length = (1/3) * (2 * π * (6.38 × 10^3 kilometers))

Finally, we can find the angular displacement:

Angular Displacement = (Arc Length) / (Radius) = [(1/3) * (2 * π * (6.38 × 10^3 kilometers))] / (6.38 × 10^3 kilometers)

Simplifying this expression will give us the answer to the problem.