Aeroplane

[neod4000]

Hello all, I am a British Maths GCSE student working towards the final exam and one day this question cropped up in a mock Maths exam I have done recently. I could not work it out and think it might have cost a percentage of the mark, and was wondering whether it would crop up again.

I try to represent it here and wonder whether any of you guys could help with offering a solution as I could not for revision purposes.

Any help concerning the answer would be greatly appreciated.
Here goes.

The Earth’s circumference around the equator is 24907.55 miles

(1 mile = 1.609344 km)

A plane flies 11km above the surface of the Earth and flies westward following the line of the equator. If the Plane is travelling at 510km per hour, how long will it take for the plane to reach the same place above the Earth’s surface from where it started from? (i.e. at the beginning of the question)

I think you have to consider the rotation of the Earth and km vs miles.
And I think the solution lies in finding the radius of the Earth and adding 11km to it, but I'm not sure.
When it says "the same place above the surface", I believe it is talking about the same place over the Earth's surface at the beginning and at the end as opposed to a complete circumnavigation of the Earth.
i.e. Over Australia at the beginning and at the end.

Any help with this would be greatly appreciated.

[KatieB]

Change 24907.55 miles to km first

by doing 24907.55x1.609344 = 40084.81615 km

Now the radius = 40084.81615 +11 = 40095.81615 km

Now get the distance the plane flies as the circumference of this new circle

dist = 2x(pie)xradius = 2x(pie)x40095.81615 = 251929.4429 km

So time = dist / speed = 251929.4429 / 510 = 493.9792998 hours

Hope that helps.

[Jimi]

Katie

I think you mean the circumference of the Earth around its equator is 40084.81615 km, not the radius.
The radius will be: 40084.81615/2π = 6379.70 km
If we now add the 11 km for the height of the plane we get:
6390.70 km.
The circumference of this new circle will be: (2π x 6390.70) km = 40153.93 km
I'm pretty sure we can ignore the Earth's rotation as the plane is revolving along with the Earth, so the time will be:
40153.93/510 = 78.73 hours.

[KatieB]

Your right Jimi,

what an idiot. I tell my students to read a question carefully and I mess up!