A plane leaves an airport X,20.6degree east and 36.8 degree north,and flies due south along the same longitude for 8hrs at the rate of 1000km/h to another airport Y,20.6 degree east and tita degree south.the plane then flies west to another airport Z for 8hrs at the same speed. Calculate,
(a) the value of tita
(b)the longitude of Z
THE ANGLE OF A SECTOR OF CIRCLE OF A RADIUS 9CM IS 120.CALCULATE THE PRIMETER OF THE SECTOR CORRECT TO THREE SIGNIFICANT OF FIGURES.(TAKE=22/7)
Perimeter of a sector = 2r +:)/360 * 2 * 22/7 * r Hence, 2*9+120/360*2*22/7*9= 18 +120 *2 * 22 *9/2520 =18 +47520/2520 = 18+18.86 = 36.86cm
(a) Well, let's see here. The plane flew due south for 8 hours from point X to point Y. If we assume that the plane maintained a constant speed of 1000 km/h, then the distance it traveled would be equal to 1000 km/h * 8 hours = 8000 km.
Now, we know that the plane started at 36.8 degrees north at point X, and it ended up at point Y, which is "tita" degrees south. Given that it traveled a distance of 8000 km due south, we can use this information to determine the value of "tita".
If we assume that the Earth is a perfect sphere, we can calculate the difference in latitude between point X and point Y using the formula:
Distance (arc length) = Radius of the Earth * angle in radians
Since we're dealing with degrees, we need to convert the angles to radians. There are 180 degrees in pi radians, so 1 degree is equal to pi/180 radians.
Angle in radians = Angle in degrees * (pi/180)
So, in our case:
Distance = Radius of the Earth * (tita degrees * (pi/180) - 36.8 degrees * (pi/180))
Since the plane flew due south, the difference in latitude is simply the absolute value of the distance. In other words:
Distance = |Radius of the Earth * (tita degrees * (pi/180) - 36.8 degrees * (pi/180))|
But we've already established that the distance is 8000 km, so we can equate the two expressions:
|Radius of the Earth * (tita degrees * (pi/180) - 36.8 degrees * (pi/180))| = 8000 km
We can now solve for "tita".
Note: The actual value of "tita" depends on the specific definition of the Earth's radius and shape. But we can use average values for a rough estimation.
(b) The longitude of airport Z is the same as airport X, which is 20.6 degrees east. The plane flew westward for 8 hours at a constant speed of 1000 km/h. Therefore, the distance it traveled longitudinally would be equal to 1000 km/h * 8 hours = 8000 km.
So, the longitude of airport Z is 20.6 degrees east.
To solve this problem, we need to break it down into two parts: the latitude and the longitude.
(a) Calculating the value of tita:
- The plane starts at point X, which is at 36.8 degrees north. It then flies directly south along the same longitude for 8 hours at a constant speed of 1000 km/h.
- Since it flew south, the latitude would decrease. We can calculate the change in latitude using the formula: velocity = distance/time.
- In this case, the plane traveled for 8 hours at a constant speed of 1000 km/h. So, the total distance covered would be 8 * 1000 = 8000 km.
- Given that the distance traveled south is equal to the change in latitude, we can calculate tita using the formula: change in latitude = distance traveled south.
- Therefore, tita = 36.8 - 8000 = -7963.2 degrees.
(b) Calculating the longitude of Z:
- The plane reaches point Y, which is at 20.6 degrees east and has a latitude of tita degrees south.
- Then, the plane flies west to another airport, Z. Since we are moving along the same latitude, there would be no change in latitude.
- The plane flies for 8 hours at a constant speed of 1000 km/h, so the distance covered would be 8 * 1000 = 8000 km.
- However, we need to find the longitude of Z. To do this, we need to calculate the arc length traveled during the 8-hour flight.
- The formula for arc length is: arc length = radius * angle (in radians).
- In this case, the radius of the Earth is irrelevant, but the angle can be calculated using the formula: angle = distance/radius.
- The distance traveled is 8000 km, and we assume the radius of the Earth is 6371 km (mean radius).
- Therefore, the arc length traveled would be: arc length = 8000/6371 = 1.255 radians.
- Next, we can calculate the change in longitude by converting the arc length in radians to degrees: change in longitude = (arc length in radians) * (180/π).
- Using the value of pi (approximately 3.1416), we can solve for the change in longitude: change in longitude = 1.255 * (180/3.1416) ≈ 71.71 degrees.
- Since the plane started at 20.6 degrees east, the longitude of Z can be found by subtracting the change in longitude from the starting longitude: longitude of Z = 20.6 - 71.71 ≈ -51.11 degrees east.
Therefore, the value of tita is approximately -7963.2 degrees, and the longitude of Z is approximately -51.11 degrees east.
8 hours at 1000km/hr = 8000km.
The circumference of the earth is roughly 40000km, so the trip was 1/5 of the way around, or 72°.
The plane is now at 72-36.8 = 33.2° south.
At that latitude, the east-west circumference is 33470 km
8000/33470 * 360° = 86°
so, the plane is now at 86-20.6 = 59.4° west