the Earth has a radius of approximately 6400km. if the Earth rotates 2degrees, how many kilometres has it rotated from its original point (arc length)?
![opp pack](/images/users/0/1/128x128.jpeg)
2 years ago
![oobleck](/images/users/0/1/128x128.jpeg)
2 years ago
as always, s = rθ
where θ is in radians
![Step-by-Step Bot](/images/users/4852/128x128.jpeg)
8 months ago
To find the distance the Earth has rotated from its original point in terms of arc length, you'll need to use the formula for the circumference of a circle.
1. First, calculate the circumference of the Earth using the formula C = 2πr, where C is the circumference and r is the radius.
- Given that the radius of the Earth is approximately 6400 km, plug this value into the formula:
C = 2π(6400 km)
2. Calculate the total distance around the Earth by multiplying the circumference by the fraction of the Earth's rotation in degrees out of a full rotation (360 degrees).
- Convert the 2 degrees rotation to a fraction by dividing it by 360 degrees.
- Multiply the fraction by the circumference calculated in step 1.
- The formula becomes:
Distance = (2π(6400 km) / 360 degrees) * 2 degrees
3. Simplify the expression by canceling out units and performing the calculations.
- The degrees unit will cancel out in the numerator and denominator, leaving only km as the unit for the distance.
- Calculate the fraction (2π / 360) = π / 180.
- The formula now becomes:
Distance = (π / 180) * (2π(6400 km))
4. Finally, perform the multiplication to find the distance the Earth has rotated.
- Multiply π / 180 by 2π(6400 km) to get the distance in km.
The final result will give you the distance in km that the Earth has rotated from its original point.
![Explain Bot](/images/users/4931/128x128.jpeg)
7 months ago
To calculate the arc length covered by the Earth when it rotates by 2 degrees, you could use the formula:
Arc Length = (2 * π * r) * (θ/360)
Where:
- Arc Length is the distance covered along the Earth's circumference (in kilometers),
- π (Pi) is approximately 3.14159,
- r is the radius of the Earth (in kilometers), and
- θ is the angle of rotation (in degrees).
Given that the radius of the Earth is approximately 6400 km and the angle of rotation is 2 degrees, we can substitute the values into the formula to find the arc length.
Arc Length = (2 * 3.14159 * 6400) * (2/360)
Arc Length ≈ 44.6328 kilometers
Therefore, the Earth would rotate approximately 44.6328 kilometers from its original point when it rotates by 2 degrees.