Question
A. An aeroplane flies from Town A (20°N,60°E) to town B(20°N,20°E). If the journey takes six hours, calculate correct to three significant figures, the average speed of the aeroplane.
B. If it then flies due north from town B to town C away, calculate correct to the nearest degree, the latitude of town c. Use the formula distance =theta÷360
B. If it then flies due north from town B to town C away, calculate correct to the nearest degree, the latitude of town c. Use the formula distance =theta÷360
Answers
GPT-4o mini
To solve both parts of your question, we'll start with part A and then move to part B.
### Part A: Average Speed Calculation
1. **Determine the distance between Town A and Town B**
- Town A is at (20°N, 60°E) and Town B is at (20°N, 20°E).
- Both towns are located at the same latitude (20°N), so we can calculate the distance using the change in longitude only.
#### Step 1: Calculate the change in longitude
- Change in longitude = 60°E - 20°E = 40°.
#### Step 2: Convert degrees to distance
- The Earth is approximately a sphere with a circumference of about 40,075 kilometers at the equator.
- The distance for one degree of longitude can be calculated using the following formula:
\[
\text{Distance per degree} = \frac{\text{Circumference}}{360}
\]
Thus,
\[
\text{Distance per degree} = \frac{40075}{360} \approx 111.32 \text{ km/degree}
\]
#### Step 3: Total Distance
- The total distance for 40° is:
\[
\text{Distance} = 40 \times 111.32 \approx 4452.8 \text{ km}
\]
#### Step 4: Average Speed Calculation
- Given that the journey takes 6 hours, the average speed can be calculated using the formula:
\[
\text{Average Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{4452.8 \text{ km}}{6 \text{ hours}} \approx 742.13 \text{ km/h}
\]
#### Final Answer for Part A
Correct to three significant figures, the average speed of the aeroplane is approximately:
\[
\text{Average Speed} \approx 742 \text{ km/h}
\]
### Part B: Latitude Calculation for Town C
1. **Determine the latitude of Town C**
- Town B is at (20°N, 20°E).
- We need to fly due north from Town B to Town C. Since the question didn't provide a specific distance or time, we can assume we want to compute latitude angles in degrees.
2. **Understanding latitude change with distance**
- Generally, latitude changes can be calculated using the same degree distance formula as before.
Given that the Earth is divided into 360 degrees, each degree of latitude represents approximately 111 km.
Let’s assume Town C is located at some distance north of Town B, represented as `d` km north. The corresponding change in latitude would be:
\[
\text{Change in Latitude} = \frac{d}{111} \text{ degrees}
\]
For example, if it flew 111 km north, the change would be 1 degree leading us to add this to the existing latitude.
3. **Final Latitude Calculation**
- Without a specific distance, we cannot compute an exact latitude for Town C. If we assume `d` km is some distance traveled north, the new latitude would be:
\[
\text{Latitude of Town C} = 20^\circ + \frac{d}{111}
\]
Assuming you want entire degrees for the result, then you will need to specify that distance \(d\) to finalize the latitude of Town C as a numeric value.
If you have a particular distance, please provide it, and I can help you finalize the latitude calculation based on that distance. Otherwise, the answer remains as per the formula provided above.
### Part A: Average Speed Calculation
1. **Determine the distance between Town A and Town B**
- Town A is at (20°N, 60°E) and Town B is at (20°N, 20°E).
- Both towns are located at the same latitude (20°N), so we can calculate the distance using the change in longitude only.
#### Step 1: Calculate the change in longitude
- Change in longitude = 60°E - 20°E = 40°.
#### Step 2: Convert degrees to distance
- The Earth is approximately a sphere with a circumference of about 40,075 kilometers at the equator.
- The distance for one degree of longitude can be calculated using the following formula:
\[
\text{Distance per degree} = \frac{\text{Circumference}}{360}
\]
Thus,
\[
\text{Distance per degree} = \frac{40075}{360} \approx 111.32 \text{ km/degree}
\]
#### Step 3: Total Distance
- The total distance for 40° is:
\[
\text{Distance} = 40 \times 111.32 \approx 4452.8 \text{ km}
\]
#### Step 4: Average Speed Calculation
- Given that the journey takes 6 hours, the average speed can be calculated using the formula:
\[
\text{Average Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{4452.8 \text{ km}}{6 \text{ hours}} \approx 742.13 \text{ km/h}
\]
#### Final Answer for Part A
Correct to three significant figures, the average speed of the aeroplane is approximately:
\[
\text{Average Speed} \approx 742 \text{ km/h}
\]
### Part B: Latitude Calculation for Town C
1. **Determine the latitude of Town C**
- Town B is at (20°N, 20°E).
- We need to fly due north from Town B to Town C. Since the question didn't provide a specific distance or time, we can assume we want to compute latitude angles in degrees.
2. **Understanding latitude change with distance**
- Generally, latitude changes can be calculated using the same degree distance formula as before.
Given that the Earth is divided into 360 degrees, each degree of latitude represents approximately 111 km.
Let’s assume Town C is located at some distance north of Town B, represented as `d` km north. The corresponding change in latitude would be:
\[
\text{Change in Latitude} = \frac{d}{111} \text{ degrees}
\]
For example, if it flew 111 km north, the change would be 1 degree leading us to add this to the existing latitude.
3. **Final Latitude Calculation**
- Without a specific distance, we cannot compute an exact latitude for Town C. If we assume `d` km is some distance traveled north, the new latitude would be:
\[
\text{Latitude of Town C} = 20^\circ + \frac{d}{111}
\]
Assuming you want entire degrees for the result, then you will need to specify that distance \(d\) to finalize the latitude of Town C as a numeric value.
If you have a particular distance, please provide it, and I can help you finalize the latitude calculation based on that distance. Otherwise, the answer remains as per the formula provided above.