The Position of two A and B on the earth’s surface are (36°N, 49°E) and (36°N, 131°W ) respectively.
(a) The difference in long between town A and town B (2 marks)
(b)) Given that the radius of the earth is 6370, calculate the distance town A and town B.
(c) Another town, C is 840 east of town B and on the same latitude as towns A and B. Find the longitude C.
LOL, usually there are two answers, going east or going west.
However this time
49 + 131 = 180 degrees Exactly :) halfway around
so what is the circumference at 36 North latitude
c = Cat equator * cos (latitude)
c = 2 pi (6370) * cos 36 = 32,380
We want halfway around so 16,190 KILOMETERS ( sure had me confused, we do navigation in nautical miles and your answers did not make sense to me)
B is 131 west of Greenwich C is 840 (Km I assume) East of B so less west
840 km (180 degrees/16,190 km) = 9.34 degrees
131 - 9.34 = 121.66 degrees West (swam to golden state shore from point B)
(a) To find the difference in longitude between town A and town B, we need to subtract the longitude of town B from the longitude of town A.
Longitude is measured in degrees from the Prime Meridian, which is at 0°. The positive direction for longitude is eastward, while the negative direction is westward.
In this case, the longitude of town A is 49°E, and the longitude of town B is 131°W.
To convert the longitude of town B from west to east, we can add 360°. This is because there are 360° in a full circle, and adding or subtracting 360° does not change the position on the Earth's surface.
Therefore, the longitude of town B in the eastward direction is 131°W + 360° = -229°.
Now we can calculate the difference in longitude between town A and town B:
Difference in longitude = Longitude of town A - Longitude of town B
= 49°E - (-229°)
= 49°E + 229°
= 278°
So, the difference in longitude between town A and town B is 278°.
(b) To calculate the distance between town A and town B, we can use the haversine formula, which accounts for the curvature of the Earth:
Distance = 2 * Radius of the Earth * arcsin(sqrt(sin²((latitude of B - latitude of A) / 2) + cos(latitude of A) * cos(latitude of B) * sin²((longitude of B - longitude of A) / 2)))
Given:
Radius of the Earth = 6370 km
Latitude of A = Latitude of B = 36°N
Longitude of A = 49°E
Longitude of B = -229°
First, convert the longitudes to radians:
Longitude of A (in radians) = 49°E * (π/180)
Longitude of B (in radians) = -229° * (π/180)
Next, plug in the values into the haversine formula:
Distance = 2 * 6370 km * arcsin(sqrt(sin²((36°N - 36°N)/2) + cos(36°N) * cos(36°N) * sin²(((-229° * (π/180)) - (49°E * (π/180)))/2)))
Simplifying the formula, we get:
Distance = 2 * 6370 km * arcsin(sqrt(sin²(0) + cos(36°N) * cos(36°N) * sin²((-229° - 49°E) * (π/360))))
Now we can calculate the distance.
(c) To find the longitude of town C, we know that it is 840 km east of town B and on the same latitude as towns A and B.
Given:
Longitude of B = -229°
To find the longitude of C, we can add 840 km to the longitude of B:
Longitude of C = Longitude of B + 840 km
Since the longitude of B is given in degrees, we need to convert the distance of 840 km into degrees of longitude. We can use the formula:
1° of longitude = (circumference of the Earth) / 360
Circumference of the Earth = 2 * π * Radius of the Earth
Now we can calculate the circumference of the Earth and the distance in degrees:
Circumference of the Earth = 2 * π * 6370 km
Distance in degrees = (840 km / Circumference of the Earth) * 360
Finally, we can calculate the longitude of C:
Longitude of C = Longitude of B + Distance in degrees