40 degrees north runs along 146th street on the north side of Indianapolis. What is the rotational velocity of the surface of the earth at 40 degrees north?
the Earth completes one revolution in 24 hr
so, how long is the 40th parallel?
the "rotational" radius is equal to the radius of the Earth times cos(40º)
the length of the parallel (circumference) is 2π times the radius
divide the circumference by 24 hr to get the rotational velocity
To calculate the rotational velocity of the Earth's surface at a specific latitude, you can use the formula:
Rotation velocity = (2 * π * radius * cosine(latitude)) / 24
where:
- π is a mathematical constant approximately equal to 3.14159
- radius is the average radius of the Earth, which is about 6,371 kilometers
- latitude is the angle in degrees
In this case, we need to convert 40 degrees north to radians, since trigonometric functions work with radians.
To convert degrees to radians, use the formula:
Radians = degrees * (π / 180)
Let's calculate:
Radians = 40 * (π / 180) ≈ 0.6981 radians
Now, we can plug this value into the formula for rotational velocity:
Rotation velocity = (2 * π * radius * cosine(0.6981)) / 24
Using a calculator, we can find the cosine of 0.6981, which is approximately 0.7660.
Rotation velocity = (2 * π * 6,371 * 0.7660) / 24
Calculating further:
Rotation velocity ≈ 306.53 kilometers per hour
Therefore, the rotational velocity of the Earth's surface at 40 degrees north is approximately 306.53 kilometers per hour.