If a plane travels halfway round the world at an altitude of 11300m, what extra distance in km, will it fly compared with the distance measured at the surface of the Earth? The radius of the earth is approximately 6400km
you have added 11300m to the radius, so add 2pi*11300 m to the circumference. Doesn't matter how big the earth is; what matters is the increase in radius.
To calculate the extra distance the plane will fly compared with the distance measured at the surface of the Earth, we first need to determine the distance it will travel in each scenario.
1. Distance at the surface of the Earth:
The distance measured at the surface of the Earth is equal to the circumference of the Earth. The formula to calculate the circumference of a circle is C = 2πr. Given that the radius of the Earth is approximately 6400 km, we can substitute this value into the formula:
C = 2π(6400)
C ≈ 12800π km
2. Distance at an altitude of 11300m (11.3 km):
To find the distance the plane will travel at an altitude of 11.3 km, we need to calculate the circumference of the circle formed by the plane's flight path. The radius of this circle is the sum of the Earth's radius and the altitude of the plane:
r = 6400 + 11.3
r ≈ 6411.3 km
Using the formula C = 2πr, we can calculate the distance:
C ≈ 2π(6411.3)
C ≈ 40286π km
3. Extra distance:
To find the extra distance traveled compared to the distance at the surface of the Earth, we subtract the distance at the surface from the distance at the altitude:
Extra distance = Distance at altitude - Distance at surface
Extra distance = 40286π - 12800π
Extra distance ≈ 27486π km
To simplify the answer, we can use an approximation for π:
Extra distance ≈ 27486 × 3.14 km
Extra distance ≈ 86324.04 km
Therefore, the plane will fly approximately 86324.04 km further compared to the distance measured at the surface of the Earth.
To calculate the extra distance the plane will fly compared with the distance measured at the surface of the Earth, we need to find the length of the curved path the plane travels.
First, let's find the circumference of the Earth at the plane's altitude. The radius of the Earth is approximately 6,400 km, and the altitude of the plane is 11,300 m. To find the radius at the plane's altitude, we can add the Earth's radius to the plane's altitude:
Radius at plane's altitude = Earth's radius + plane's altitude
= 6,400 km + 11.3 km
Now, we can calculate the circumference of a circle with the radius at the plane's altitude:
Circumference at plane's altitude = 2 * π * (Radius at plane's altitude)
Next, we need to determine the distance the plane will fly compared with the distance measured at the surface of the Earth. The plane is traveling halfway around the Earth, so the extra distance it flies can be calculated by subtracting the circumference of the Earth's surface from the circumference at the plane's altitude:
Extra distance = Circumference at plane's altitude - Circumference at Earth's surface
Now, let's substitute the values and calculate the extra distance.
Radius at plane's altitude = 6,400 km + (11.3 km / 1000) km (converting meters to kilometers)
= 6,400 + 0.0113 km
Circumference at plane's altitude = 2 * π * (Radius at plane's altitude)
Extra distance = Circumference at plane's altitude - Circumference at Earth's surface
= 2 * π * (Radius at plane's altitude) - 2 * π * (Earth's radius)
Now, let's substitute the values of π, the radius at the plane's altitude, and the radius of the Earth, and calculate the extra distance.
Extra distance = 2 * π * (6400 + 0.0113) - 2 * π * 6400
Calculating this expression will give us the value of the extra distance in kilometers that the plane will fly compared to the surface distance.