How long would it take for the Earth to complete a full turn if a person at 56.4° northern geographical latitude floats apparently weightlessly across the room? Use REarth = 6,385 km for the radius of Earth.
To determine how long it would take for the Earth to complete a full turn while a person floats apparently weightlessly across the room, we need to consider the latitude of the person and the circumference of the Earth at that latitude.
The circumference of a circle can be calculated using the formula:
C = 2 * π * r
where C is the circumference and r is the radius of the circle.
In this case, the latitude of the person is given as 56.4° northern geographical latitude. To determine the latitude in radians, we need to convert it from degrees to radians using the formula:
radians = degrees * π / 180
Substituting the given value of 56.4°, we can calculate the latitude in radians:
latitude in radians = 56.4° * π / 180 = 0.985 radians
Next, we need to calculate the circumference of the Earth at the latitude of the person. Since the Earth is not a perfect sphere, its circumference varies with latitude. The formula for the circumference of Earth at a given latitude is:
C = 2 * π * R * cos(latitude)
where C is the circumference, R is the radius of the Earth, and latitude is the latitude in radians.
Substituting the given radius of the Earth (R = 6,385 km) and the latitude in radians (latitude = 0.985 radians), we can calculate the circumference of the Earth at that latitude:
C = 2 * π * 6,385 km * cos(0.985) = 39,148 km
Finally, to determine the time it would take for the Earth to complete a full turn while a person floats across the room, we need to divide the circumference of the Earth at that latitude by the rotational speed of the Earth. The rotational speed of the Earth is approximately 24 hours, which is equivalent to 86,400 seconds.
Time = Circumference / Rotational Speed
Time = 39,148 km / 86,400 s ≈ 0.45 km/s
Therefore, it would take approximately 0.45 kilometers per second for the Earth to complete a full turn while a person floats apparently weightlessly across the room at 56.4° northern geographical latitude.