Question

Two towns A and B. are on the same parallel of latitude 56°N, their longitudes are 45°E and 32°W respectively. If it takes an aero plane 6 hours to fly from A to B along the parallel of latitude, calculate its speed correct to the nearest kilometre per hour. (Take the radius of the earth = 6400km, π = 22 7 (8 marks)​

Answer 1

The speed of the airplane from town A to town B along the parallel of latitude is approximately 486 km/h, given a distance of 2918.91 km and a travel time of 6 hours.

To find the distance between towns A and B along the parallel of latitude, we can use the formula for the arc length of a circle:

`\[ \text{Arc Length} = \frac{\text{angle in degrees}}{360} * 2 \pi R \]`

where:

- The angle in degrees is the difference in longitudes, which is
`\(45^\circ - (-32^\circ) = 77^\circ\)`.

- R is the radius of the Earth, given as 6400 km.

`\[ \text{Arc Length} = (77^\circ)/(360) * 2 \pi * 6400 \]`

Now, calculate the arc length:

`\[ \text{Arc Length} = (77)/(360) * 2 * (22)/(7) * 6400 \]\[ \text{Arc Length} \approx (77)/(360) * 2 * (22)/(7) * 6400 \]\[ \text{Arc Length} \approx 2918.91 \, \text{km} \]`

Now, to find the speed, use the formula
`\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)`. Given that the time is 6 hours:

`\[ \text{Speed} = (2918.91)/(6) \]\[ \text{Speed} \approx 486.48 \, \text{km/h} \]`

Therefore, the speed of the airplane, correct to the nearest kilometer per hour, is approximately
`\(486 \, \text{km/h}\)`.