How long would it take for the Earth to complete a full turn if a person at 27° northern geographical latitude floats apparently weightlessly across the room? Use REarth = 6,379 km for the radius of Earth.
Help me please!
To calculate the time it takes for the Earth to complete a full turn, we need to consider the latitude of the person and the circumference of the Earth at that latitude.
First, let's calculate the circumference of the Earth at the given latitude using the formula:
C = 2 * π * R
where C is the circumference, π is approximately 3.14159, and R is the radius of the Earth.
Given that the radius of the Earth (REarth) is 6,379 km, we can substitute this value into the formula:
C = 2 * 3.14159 * 6,379 km
Calculating this gives us:
C ≈ 40,074 km
Next, we'll calculate the distance the person covers when floating across the room. This distance will be equal to the circumference of the Earth at the given latitude since the person is essentially moving along the latitude. The person's weightlessness does not affect this calculation.
Now that we know the distance the person covers (C ≈ 40,074 km) and the circumference of the Earth at the latitude (40,074 km), we can find the time it takes for a full turn.
To calculate the time, we can use the formula:
Time = Distance / Velocity
However, we don't have the velocity. We need to find the velocity first.
The velocity of the person floating across the room will depend on how long it takes them to cover the distance. We can use the formula:
Velocity = Distance / Time
Since we are trying to find the time, we rearrange the formula:
Time = Distance / Velocity
Now, let's assume that the person takes 1 hour (60 minutes) to float across the room. We can calculate the velocity:
Velocity = Distance / Time
Velocity = 40,074 km / 1 hour
Velocity ≈ 40,074 km/h
Now that we have the velocity, we can calculate the time it takes for a full turn using the formula:
Time = Distance / Velocity
Time = 40,074 km / 40,074 km/h
Time = 1 hour
Therefore, it would take around 1 hour for the Earth to complete a full turn if a person at 27° northern geographical latitude floats apparently weightlessly across the room.