|MadSci Network: Physics|
Hey, Joe! The way I see, It's a pure geometrical question, not Physics. Look at the picture. We want to know the length of the arc AB. We only need to know the angle which determines the arc, so l = .R , where R is the Earth radius. R is aproximatelly equal to 6.400 km, but I don't know this value on ft , so itís an exercise to you. The angle is easy to determine. Note that cos (/2) = R/(R+h). The angle is exactly /2 because the two triangles are equivalent. With a calculator, you can imediatelly obtain . However, you can use this relation Cos (/2) = ( (1+ cos ) / 2 )Ĺ to take directly the cos . You may want to know that I did a rough aproximation on solving this question. I put the plane to travel right above the equator line, following its direction, because at that point the section (cut) of the Earth is a circle with R=6.400 km. If the plane, for instance, were travelling perpendicularly to equator, the section would be na elipsis, but I think my way is a reasonable aproach for what you need. Hope this helps. D..! Any doubts to email@example.com
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