An aeroplane flies from town A(20°N,60°E) to town B(20°N,20°E) if the journey takes 6hours, calculate, correct to 3 significant figure, the average speed of the aeroplane.
Change in longitude =60-20=40°=40π/180
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Distance travel from A to be C in the arc=(40π/180)6400)cos(lat)
Where the latitude is the same 20°
Average speed=(total distance)/total time
To calculate the average speed of the airplane, we need to find the distance between town A and town B first.
The latitude of both towns is the same (20°N), so we only need to consider the longitude difference. The longitude of town A is 60°E, and the longitude of town B is 20°E. To find the distance, we subtract the longitude of town B from the longitude of town A:
60°E - 20°E = 40°
Since we are traveling along the same latitude, we can treat the distance as a straight line.
Now, we need to calculate the distance covered in 6 hours. Speed is equal to distance divided by time. Therefore, the speed is the distance divided by the time taken:
Speed = Distance / Time
Speed = 40° / 6 hours
Speed = 6.67°/hour
To round to 3 significant figures, we have:
Speed ≈ 6.67°/hour
To calculate the average speed of the airplane, you need to find the distance between town A and town B, and then divide it by the time taken during the journey.
Step 1: Find the distance between town A and B.
The distance between two points (latitude and longitude) on the Earth's surface can be calculated using the Haversine formula. But since both points have the same latitude, the calculation becomes simpler.
The distance between two points with the same latitude can be calculated using the formula:
Distance = Longitude of B - Longitude of A
Given:
Longitude of A = 60°E
Longitude of B = 20°E
Distance = 20°E - 60°E
Distance = -40°E
Step 2: Convert the negative longitude into positive longitude.
Since the longitude is measured in the range of -180° to +180°, we need to convert the negative longitude into a positive one.
Positive Longitude = 360° - |Negative Longitude|
Positive Longitude = 360° - |-40°E|
Positive Longitude = 360° - 40°E
Positive Longitude = 320°E
Step 3: Calculate the average speed.
Now that we have the distance between town A and B, we can calculate the average speed using the formula:
Average Speed = Distance / Time
Given:
Distance = Positive Longitude = 320°E
Time = 6 hours
Average Speed = 320°E / 6 hours
Average Speed = 53.3333...°E/hour
Rounding to three significant figures, the average speed of the airplane is approximately 53.3°E/hour.