# The helicopter position?

Helicopter fly from New Jersey to the north for 500 km and then to the east 500 km, then to the south 500 km and then to the west 500 km where is she now?

Can it arrive at a position where everywhere is south?

• What does "where everywhere is a south" mean? – Rand al'Thor Mar 8 '18 at 12:48
• @JamesWebster But wouldn't that mean the question is obvious because New Jersey is too far from the North Pole? – Rand al'Thor Mar 8 '18 at 12:57
• @Randal'Thor the second question is about interpreting it – Obvious Mar 8 '18 at 13:00

Since we know that earth is not flat, I'll answer :

over the Atlantic ocean

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• I understand the accepted answer, but I still don't see how this fits "a position where everywhere is south." Can anyone clear that up for me? – Pugmonkey Mar 8 '18 at 16:10

Assuming no fuel issues, the helicopter is about 37 km east of its starting position.

New Jersey is roughly on the 40th parallel, and 500km is about 1/80 of the way around the world (according to the old definition of the metre, it's exactly so), so the point 500 km to the north of NJ is roughly at latitude 44.5°N.

The length of a latitudinal circle is directly proportional to the cosine of the latitude, so the length of the northern latitudinal circle is $\frac{cos(44.5°)}{cos(40°)} \approx 0.93$ times that of the NJ's latitudinal circle.

Therefore, the 500 km east are scaled up to 537 km during the southward portion of the trip, from which you can subtract the 500 km to arrive at the solution.

If you travel 40-ish km east from a point in New Jersey, you are either still in New Jersey, in New York, or somewhere over the Atlantic ocean.

• Showoff :-) – Rand al'Thor Mar 8 '18 at 13:52

I would say

it crashed, because there's no way an helicopter can fly 2000km without refill

also "everywhere is a south" means

north pole, because at north pole, whatever the direction you look at, you will be facing south

• No, it won't crash or run out of fuel. It was a CH-53E Super Stallion that was refueled in-flight from a KC-130T Hercules. Look, Elon even sent his car along for this ride. Older variants like the Canadian CH-124 Sea King can land on water. The UH-60 Blackhawk has a ferry range of 2220 KM. – Amit Naidu Mar 9 '18 at 13:05

I'd say :

In the Atlantic Ocean because the earth is not flat. The 500km move to the east closer to the pole is not equivalent to the movement to the west: the helicopter should be more in the east than initially.

• Yes, this is correct. – Rand al'Thor Mar 8 '18 at 13:42