A moving object takes off from a town p(latitude 40°N ,longitude 52°E) and after flying 1450km due East,it reaches a town Q.it then flies due North to another town S on latitude 60°N.
1)Calculate the longitude Q
2)The distance Q and S along the parallel of longitude (take r=6400km ,π=3.142?
One minute around the equator that is.
1) To find the longitude of town Q, we need to calculate the distance it has moved eastward from the starting point.
Since the object flew due East for 1450km, we can use the formula:
Distance = (Longitude in degrees) x (π/180) x r
where r is the radius of the Earth. Given r = 6400km, we can rearrange the formula to solve for Longitude:
Longitude in degrees = Distance / ((π/180) x r)
Substituting the values, we get:
Longitude in degrees = 1450 km / ((3.142/180) x 6400 km)
Longitude in degrees ≈ 1450 km / (0.05515) ≈ 26,279.0512 degrees
However, since we are calculating longitude relative to the prime meridian (0°), we need to convert our result to a value between -180° and +180°. Therefore:
Longitude Q ≈ 26,279.0512 degrees - 360° ≈ -333.9488 degrees
So, the longitude of town Q is approximately -333.95°.
2) To calculate the distance between towns Q and S along the parallel of longitude, we can use the formula:
Distance = (Latitude in degrees) x (π/180) x r
Given that the latitude of town S is 60°N, we can substitute the values into the formula:
Distance = 60° x (π/180) x 6400 km
Distance = 60° x (3.142/180) x 6400 km ≈ 666.33 km
Therefore, the distance between towns Q and S along the parallel of longitude is approximately 666.33 km.
To calculate the longitude of town Q, we need to consider that the object started from town P, which has a longitude of 52°E. It then flew due east for 1450 km. Since the Earth is divided into 360° of longitude, and the object traveled 1450 km, we can calculate the change in longitude using the following formula:
Change in longitude = (distance traveled / circumference of Earth at the given latitude) * 360°
The circumference of the Earth at the given latitude can be calculated using the formula:
Circumference of Earth at given latitude = 2 * π * radius of Earth * cos(latitude)
1) Calculate the longitude Q:
First, let's calculate the circumference of the Earth at latitude 40°N:
Circumference of Earth = 2 * π * 6400 km * cos(40°)
Using the given value of π ≈ 3.142, the equation becomes:
Circumference of Earth = 2 * 3.142 * 6400 km * cos(40°)
Next, we can calculate the change in longitude:
Change in longitude = (1450 km / Circumference of Earth) * 360°
Substituting the calculated value for the circumference of the Earth:
Change in longitude = (1450 km / (2 * 3.142 * 6400 km * cos(40°))) * 360°
Calculating this expression will give us the change in longitude. To find the longitude Q, we need to add this change to the initial longitude of town P (52°E).
2) Calculate the distance Q and S along the parallel of longitude:
The distance Q and S along the parallel of longitude can be calculated using the formula:
Distance = arc length = radius of Earth * latitude * (π / 180°)
First, let's calculate the distance Q along the parallel of longitude:
Distance Q = 6400 km * 60° * (π / 180°)
Next, we can calculate the distance S along the parallel of longitude:
Distance S = 6400 km * 40° * (π / 180°)
By evaluating these equations, we can find the distances Q and S along the parallel of longitude.
You try first
You told me earlier that it was about 40,000 km around great circle. Here you call it 40,213
Then it would be 40,213 * cos (latitude) to go 360 degrees around a particular latitude.
To proceed along a particular longitude would of course be 40,213/360 km/degree