Airplane around the equator

[teddef21]

1. A)How fast and in what direction would an airplane need to fly(relatively close to the ground) around the equator to always stay in sunlight or darkness?
B) How fast and in what direction would an airplane need to fly at 40 degrees North Latitude to always stay in sunlight or darkness?Im having trouble figuring out what equation would be best to use for this problem. I am new in physics and am pretty mathmetically challenged so any help would be greatly appreciatied

 

[mgb_phys]

The simplest case is assume it flys around the equator at the same speed the Earth rotates, so it always has the same local (sun) time.
Then you just need the cicumference of the Earth (hint definition of the metre) and the time taken for the Earth to rotate (for extra credit - this isn't 24hours).

For 40deg lat just work out what the diamter of Earth is at that latitude, it only involves drawing a triangle.

To make it more complicated, you could assume it takes off at dawn and lands in the same place just before dusk, it would still have been in sunlight but doesn't need to have flown as fast. This might be overcomplicating the question for a beginner class.

 

[ogb p]

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I would approach this problem by using basic principles of geometry and the rotation of the Earth. The Earth rotates at a constant rate of 15 degrees per hour, or one full rotation every 24 hours. This means that any point on the equator will experience 12 hours of sunlight and 12 hours of darkness.

For part A, the airplane would need to fly at the same speed as the rotation of the Earth, which is approximately 1670 kilometers per hour (equivalent to 1037 miles per hour). This would allow the airplane to stay at the same longitude and continually experience sunlight or darkness. The direction of flight would also need to be eastward, following the direction of the Earth's rotation.

For part B, the airplane would need to fly at a slower speed than the rotation of the Earth, since it is located at a higher latitude. The exact speed would depend on the specific latitude, but it would need to be slower than 1670 kilometers per hour. The direction of flight would also need to be eastward, following the direction of the Earth's rotation.

In summary, the key factor for staying in sunlight or darkness while flying around the equator or at a specific latitude is to match the speed of the Earth's rotation and to fly in the same direction. This can be achieved by using a combination of altitude and airspeed adjustments.