An aircraft flew due west from point A (39.64^ exto extN, 50^ exto extE) to B (39.64^ exto extN, 20^ exto…

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An aircraft flew due west from point A (39.64^ exto extN, 50^ exto extE) to B (39.64^ exto extN, 20^ exto extW). The aircraft flew along a small circle of latitude. Calculate the distance covered by t

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6. An aircraft flew due west from point A $(39.64^\circ \text{N}, 50^\circ \text{E})$ to B $(39.64^\circ \text{N}, 20^\circ \text{W})$ .
The aircraft flew along a small circle of latitude.

Identify the given values.
Latitude, $\theta = 39.64^\circ$ .
Longitude of A $= 50^\circ \text{E}$ .
Longitude of B $= 20^\circ \text{W}$ .
Radius of Earth, $R = 6370 \text{ km}$ .
$\pi = \frac{22}{7}$ .
Calculate the difference in longitude, $\alpha$ .
Since one longitude is East and the other is West, we add their magnitudes.
$\alpha = 50^\circ + 20^\circ = 70^\circ$
Use the formula for the distance along a small circle
$D = \frac{\alpha}{360^\circ} \times 2 \pi R \cos \theta$ .
$D = \frac{70}{360} \times 2 \times \frac{22}{7} \times 6370 \times \cos(39.64^\circ)$
Calculate $\cos(39.64^\circ)$ .
$\cos(39.64^\circ) \approx 0.7700$
Substitute the value and calculate the distance.
$D = \frac{70}{360} \times 2 \times \frac{22}{7} \times 6370 \times 0.7700$ $D = \frac{7}{36} \times \frac{44}{7} \times 6370 \times 0.7700$ $D = \frac{44}{36} \times 6370 \times 0.7700$ $D = \frac{11}{9} \times 6370 \times 0.7700$ $D \approx 1.22222 \times 6370 \times 0.7700$ $D \approx 7780.44 \times 0.7700$ $D \approx 5990.9388 \text{ km}$
Round the distance to the nearest km.
$D \approx 5991 \text{ km}$
The distance covered by the aircraft is:
$\boxed{5991 \text{ km}}$
7. In the given figure, A, B, C, D, and E are points

An aircraft flew due west from point A (39.64^ exto extN, 50^ exto extE) to B (39.64^ exto extN, 20^ exto extW). The aircraft flew along a small circle of latitude. Calculate the distance covered by t

Answer

Step-by-step solution

Identify the given values.

Calculate the difference in longitude, $\alpha$ .

Use the formula for the distance along a small circle

Calculate $\cos(39.64^\circ)$ .

Substitute the value and calculate the distance.

Round the distance to the nearest km.

Try one yourself

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More Geography Questions

An aircraft flew due west from point A (39.64^ exto extN, 50^ exto extE) to B (39.64^ exto extN, 20^ exto extW). The aircraft flew along a small circle of latitude. Calculate the distance covered by t

Answer

Step-by-step solution

Identify the given values.

Calculate the difference in longitude, α\alphaα.

Use the formula for the distance along a small circle

Calculate cos⁡(39.64∘)\cos(39.64^\circ)cos(39.64∘).

Substitute the value and calculate the distance.

Round the distance to the nearest km.

Try one yourself

Still stuck on this one?

More Geography Questions

Calculate the difference in longitude, $\alpha$ .

Calculate $\cos(39.64^\circ)$ .