How long would it take for the Earth to complete a full turn if a person at 43.8° northern geographical latitude floats apparently weightlessly across the room? Use REarth = 6,390 km for the radius of Earth.
To determine how long it would take for the Earth to complete a full turn while a person at a specific latitude floats apparently weightlessly across the room, we need to consider the rotational period of the Earth.
The Earth rotates once on its axis in approximately 24 hours, which is why we have a day and night cycle. However, due to the Earth's shape, the rotational speed is not constant at different latitudes. The closer you are to the poles, the slower the rotational speed due to the smaller circumference of those latitudes.
To calculate the time it takes for the Earth to complete a full turn at a specific latitude, we need to know the circumference of that latitude. We can determine the circumference of a circle using the formula:
Circumference = 2 * π * Radius
Since the radius of the Earth is given as REarth = 6,390 km, we can calculate the circumference of the latitude the person is at:
Circumference = 2 * π * REarth * cos(latitude)
In this case, the latitude is 43.8°. We need to convert it to radians before calculating the cosine:
Circumference = 2 * π * REarth * cos(43.8° * π/180)
Now, we divide the circumference by the speed at which the person floats across the room to determine the time it takes for the Earth to complete a full turn. Unfortunately, the speed at which the person floats across the room is not provided in the question. If you have that information, you can substitute it into the calculation to get the answer.
So, the time it takes for the Earth to complete a full turn at the given latitude will depend on the speed at which the person floats across the room.