The length of the equator of the earth is40000 km .A plane flies once round the earth at a height of 1 km above the equator. the total distance which the plane travels is( with an error of less than 1 km)?
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Answer:
Since the earth is round, would a plane flying at 38,000' have a longer distance to travel than a vehicle would taking the same path on the ground?
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Yes and no (but read on).
Note that the Earth is oblong, not round. Earth has an equatorial diameter of 12,756 km (7,926 mi), and a polar diameter of 12,713.6 km (7,899.86 mi). So the Earth is shorter pole-to-pole than around its equator. That said, you'd be traveling around the circumference of the Earth, not the diameter.
The Earth has a polar circumference of 24,859 miles (24,901 miles equatorially). That's an average of course and doesn't factor in geographical features like mountains and valleys, so your land journey would be much further, irrespective of which direction you headed, if your
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Yes. But the other answers explain the advantages that offset the distance.
Do the math yourself.
The earth is roughly 24,000 miles in diameter.
It's Diameter is roughly 8000 miles.
Diameter divided by 2 equals radius.
Radius times 2 times pi equals circumference.
Add 38,000 feet to the radius and recompute the circumference.
That difference between 24,000 miles and your new circumference is the increase in circumference.
Divide that by the actual circumference and get a % increase.
An interseting excercise, but it presumes the aircraft goes up vertically up to 38,000 feet then vertically down at the end, instead of varying altitudes.
IF you ignore the 38,000ft ascend and 38,000 ft descend, then following will be the calculation.
Car will definitely follow the arc length S, while traveling on the globe, while since, air craft is air-borne it is not mandatory that it will follow a curve, and may fly straight. So for land distance of 1000 Miles which will be traveled by car, the aerial distance will be 996 Miles.
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Why doesn't an airplane traveling in the opposite direction of the Earth's rotation move faster than one traveling in the same direction of the Earth's rotation?
Why can't an airplane fly above the ground, stay there and let the Earth pass underneath, and then land when the destination arrives?
If the earth were spherical, would planes fly into space if they flew in a straight line?
38,000⋅2π feet farther on a round the world trip.
But that is a rounding error in the context of the journey.
Other things to consider. The plane can fly a straight line from A to B. The ground journey follows roads and will be less direct. Advantage airplane.
The plane only gets you from airport to airport, not door to door. Advantage auto.
Yes, it would be longer. But how much?
The diameter of the earth is approximately 7920 miles.
Flying at 38,000 feet adds an additional 7.2 miles to the radius, 14.4 miles to the circumference.
That’s only about .2% extra distance on a great circle route. That works out to two extra miles on a 1000 mile trip.
That’s more than made up for by the greatly increased efficiency of jet airplanes flying at cruising altitude.
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It would. It is not as big a distance as the difference in the radii would suggest. Airplanes follow what are called great circle routes. They cut off part of the altitude increase by following an arc when viewed from above normal to the earth.
YES. it is obvious.
the radius of earth is 6400 km and taking that radius if we calculate the circumference given by 2*pie*r for the car traveling on the surface.
the radius of earth will be more for the plane at 38,000 feet which is approx 12 km more plus the radius 6400 km.
so if we calculate taking the radius from center with r = 6412 this time.
the plane will travel a longer distance.