What is the linear speed of a point at a latitude of 18.0 N?
To determine the linear speed of a point at a specific latitude, we need to use the formula for calculating the Earth's rotational speed at a given latitude. The linear speed, also known as the tangential speed, represents how fast an object is moving along a circular path.
The formula for calculating the linear speed at a specific latitude is:
v = r * ω * cos(φ)
Where:
v is the linear speed,
r is the radius of the Earth (approximately 6,371 kilometers),
ω is the angular velocity of the Earth's rotation (approximately 7.2921159 x 10^-5 radians per second),
φ is the latitude in radians.
However, since we are given a latitude in degrees, we need to convert it to radians. The formula to convert degrees to radians is:
radians = (π/180) * degrees
So, to find the linear speed at a latitude of 18.0 N, we will follow these steps:
1. Convert the latitude from degrees to radians:
radians = (π/180) * 18.0
2. Substitute the values into the formula:
v = 6,371 km * (7.2921159 x 10^-5 radians per second) * cos(radians)
3. Calculate the value:
v = 6,371 km * (7.2921159 x 10^-5 radians per second) * cos(radians)
Note: The value of the cosine of the latitude in this formula represents the cosine of the converted radians.
By following these steps, you can calculate the linear speed of a point at a latitude of 18.0 N.