The Earth moves toward you through what distance? (Assume the seat is 45.0 cm high.)
To determine the distance that the Earth moves toward you, we need to consider the scale of the Earth's movement relative to your position.
Given that the seat height is provided as 45.0 cm, we can assume that you are sitting on the seat, observing the Earth move towards you.
However, it is important to note that the Earth's movement towards you is negligible in most situations, as the Earth's motion is primarily governed by its rotation and revolution around the Sun.
If we were to consider the average distance between the Earth and an individual, which is approximately 6,371 km (radius of the Earth), we can estimate the maximum movement of the Earth towards a person using basic trigonometry.
We can use the tangent function to calculate the distance by considering the angle from your eyes to the horizon and the height of the seat:
tan(angle) = opposite/adjacent
In this case, the angle between your eye and the horizon is small, so we can approximate it with a small angle, and the opposite side is the change in the Earth's distance towards you (which we want to find), and the adjacent side is the radius of the Earth.
To simplify calculations, we can convert the seat height from centimeters to kilometers:
45.0 cm = 0.45 meters = 0.00045 kilometers
Now, plugging in the values, we have:
tan(angle) = change in Earth's distance (opposite) / radius of the Earth (adjacent)
tan(angle) ≈ change in Earth's distance / 6,371 km
Assuming a tiny angle, we can approximate that the tangent of the angle is equal to the angle:
angle ≈ change in Earth's distance / 6,371 km
We can rearrange the equation to isolate the change in Earth's distance:
change in Earth's distance ≈ angle * 6,371 km
Given the small angle approximation, it becomes:
change in Earth's distance ≈ height of the seat / 6,371 km
Substituting the seat height we were given:
change in Earth's distance ≈ 0.00045 km / 6,371 km
Simplifying, we get:
change in Earth's distance ≈ 7.07 * 10^-8 km
So, the Earth moves toward you through a distance of approximately 7.07 * 10^-8 kilometers (or 0.0707 millimeters) based on the given seat height of 45.0 cm. However, it's important to note that this distance is extremely small and practically negligible.