Assume that here in sussex we live at exactly latitude 45 degress. Calculate the tangential speed, in m/sec and in mph that we are rotating at
To calculate the tangential speed at a specific latitude on Earth, we need to use the following formula:
Tangential Speed = (2 * π * Radius of Earth * Cosine of Latitude) / Time
First, let's determine the radius of the Earth. The mean radius of the Earth is approximately 6,371 kilometers or 6,371,000 meters.
Now, we can substitute the given latitude, radius, and time into the formula.
Latitude: 45 degrees
Radius of Earth: 6,371,000 meters
Time: 24 hours or 86,400 seconds (one complete rotation of Earth)
Using the equation above, the calculation for tangential speed in meters per second is:
Tangential Speed = (2 * 3.14 * 6,371,000 * cos(45)) / 86,400
Calculating the equation gives:
Tangential Speed ≈ 465.1 meters per second
To convert this to miles per hour (mph), we can use the conversion factor that 1 meter per second is approximately equal to 2.237 miles per hour.
So, the calculation for tangential speed in mph is:
Tangential Speed (in mph) ≈ 465.1 * 2.237
Calculating the equation gives:
Tangential Speed (in mph) ≈ 1040.7 mph
Therefore, at precisely latitude 45 degrees in Sussex, the tangential speed is approximately 465.1 meters per second (m/s) and approximately 1040.7 miles per hour (mph).