what is the linear velocity of a point in Sydney, Australia which is at latitude 33deg 55'S. Radius of earth is 6370km.
To calculate the linear velocity of a point on the Earth's surface, we need to take into account the rotation of the Earth. The linear velocity is the velocity of an object as it moves in a straight line, so we are looking for the velocity of a point due to the Earth's rotation.
To find the linear velocity of a point, we need to calculate the angular velocity first. The angular velocity is the rate at which an object rotates around an axis. In this case, the axis is the Earth's rotation axis.
The Earth completes one full rotation every 24 hours, which can be expressed as 360 degrees per 24 hours. So, the angular velocity of the Earth is:
Angular Velocity = 360 degrees / 24 hours
Now, we need to find the linear velocity at a specific latitude. The linear velocity can be calculated using the formula:
Linear Velocity = Angular Velocity × Radius of the Earth × Cos(latitude)
In this case, the radius of the Earth is given as 6370 km, and the latitude of Sydney, Australia is 33 degrees 55 minutes south (33° 55' S). However, we need to convert this latitude into decimal degrees. To do this, we divide the number of minutes by 60:
33 degrees + (55 minutes / 60) = 33° + (55/60)° = 33° + 0.92° = 33.92°
Now that we have the latitude in decimal degrees, we can calculate the linear velocity:
Angular Velocity = 360° / 24 hours = 15° per hour
Linear Velocity = (15° per hour) × (6370 km) × Cos(33.92°)
By plugging these values into a calculator, we can find the answer.