An aeroplane flies from town A(20°N,60°E) to townB (20°N,20°E)
if the journey takes 6 hours
Calculate correct to 3 significant figures, the average speed of the aeroplane
If it then flies due north from town B to town C 420km away.calculate to the nearest degree the latitude of town C
No formula
No formula
Student
Why did the airplane go to therapy? Because it had altitude issues!
To calculate the average speed of the airplane from town A to town B, we need to find the distance traveled. Since the two towns are located at the same latitude (20°N), we can calculate the distance using the longitude difference.
The longitude difference can be calculated by subtracting the longitude of town B (20°E) from the longitude of town A (60°E).
Longitude difference = 60°E - 20°E
= 40°
Since the journey takes 6 hours, we can calculate the average speed using the formula:
Average speed = Distance / Time
We know that the distance traveled is equal to the circumference of the Earth at the given latitude. The Earth's circumference at 20°N is approximately 40,075 km. Therefore, the distance traveled is:
Distance = (40 / 360) * 40,075 km (since the longitude difference is 40° out of 360°)
Plugging in the values:
Distance = (40 / 360) * 40,075 km
= 4,452.78 km
Now we can calculate the average speed:
Average speed = Distance / Time
= 4,452.78 km / 6 hours
= 742.13 km/h
Therefore, the average speed of the airplane is approximately 742.13 km/h.
Now, let's calculate the latitude of town C, which is 420 km away and due north from town B.
Since town C is due north of town B, their latitudes will be the same. Therefore, the latitude of town C is also 20°N.
To calculate the average speed of the airplane, we need to use the formula:
Average speed = Total distance / Total time
First, let's calculate the distance between town A and town B. The distance between two points on the Earth's surface can be calculated using the Haversine formula or the Spherical law of cosines. However, since the points are relatively close, we can use the Pythagorean theorem to get an approximate distance.
Given that the latitude of town A (20°N) is the same as the latitude of town B (20°N), we can assume that the airplane flies along a parallel line. The difference in longitude (60°E - 20°E = 40°) represents the width of the triangle formed between the two towns.
Using the Pythagorean theorem, the distance between town A and town B is:
d = √[(longitude difference)² + (latitude difference)²]
d = √[(40°)² + (0°)²]
d ≈ √(1600 + 0)
d ≈ √1600
d ≈ 40
So, the distance between town A and town B is approximately 40 km.
Now, we can calculate the average speed:
Average speed = Total distance / Total time
Average speed = 40 km / 6 hours
Average speed ≈ 6.667 km/h
Therefore, the average speed of the airplane is approximately 6.667 km/h (to 3 significant figures).
Next, let's calculate the latitude of town C. Since the airplane flies due north from town B to town C, the latitude of town C will remain the same as the latitude of town B. Therefore, the latitude of town C is also 20°N.
Hence, the latitude of town C is approximately 20°N (to the nearest degree).
Approximate the earth as a perfect sphere, with radius 6371 km.
Change in longitude = 60-20 = 40° = 40π/180 radians
Latitude of flight path = 20° N
horizontal radius = Rcos(20°)
Horizontal arc length from A to B
=Rcos(20°)(40π/180)
=6371*0.9397*.6981
=1506.6 km
1506.6 km took 6 hours, so
average ground speed
=1506.6/6
=251.1 km/hr
travelling due north another 420 km subtends an angle
=420/6371 radians
=0.06593 radians
=0.06593*180/π °
=3.78°
Latitude of town C
=20+3.78
=23.78°N