X and Y both lie on the equator and their longitude differ by 25°. Find the distance between X and Y along the equator, to the nearest unit .
Take radius of earth=6400km and π= 3.142
We know that the equator is a circle of radius 6400 km around the earth. Therefore, the circumference of the equator is 2πr = 2(3.142)(6400) = 40,320 km.
Since X and Y both lie on the equator, the distance between them along the equator is simply the arc length between their longitudes. The difference in longitudes between X and Y is 25°.
To find the arc length between these two longitudes, we need to find what fraction of the circumference of the equator corresponds to a difference of 25°. Since there are 360° around the equator, we can set up a proportion:
25/360 = x/40,320
Solving for x, we get:
x = (25/360) * 40,320 = 2800 km (rounded to the nearest unit)
Therefore, the distance between X and Y along the equator is approximately 2800 km.
To find the distance between X and Y along the equator, we need to find the circumference of the earth and then calculate the fraction of the circumference that is equivalent to a 25° longitude difference.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.
Given that the radius of the earth is 6400 km and π is 3.142, we can calculate the circumference of the earth as follows:
C = 2 × 3.142 × 6400 km
C ≈ 40192 km
Now, we need to find the fraction of the circumference that corresponds to a 25° longitude difference. There are 360° of longitude in a full circle, so one degree of longitude covers 1/360th of the circumference.
To find the fraction corresponding to 25°, we can set up the following proportion:
25° / 360° = x / 40192 km
Cross-multiplying, we get:
360x = 25 × 40192 km
360x ≈ 1004800 km
Dividing both sides by 360, we find:
x ≈ 2791.1 km
Therefore, the distance between X and Y along the equator, to the nearest unit, is approximately 2791 km.