From Donetsk the plane flew 450 km north, then 450 km east, then 450 km south and 450 km west. Will the plane get back to Donetsk?

1) Donetsk – 48o east longitude, 38o east longitude
450 km: 111.2 km (length 1o of the meridian at this latitude) = 4o – the plane will fly to the north.
2) Turning to the east, the plane flew along 52o N. (48o + 4o = 52o)
The arc length is 1 ° parallel at 52 ° N latitude. = 68.8 km
We find out how many degrees the plane moved east along 52о N, having flown 450 km:
450: 68.8 = 6.5o
3) 6.5о × 68.8 km = 447.2 km – the plane flew east along 52о N
4) Turning to the south, the plane flew 450 km and again got to 48 ° latitude, where the arc length is 1о = 74.6 km.
6.5о × 74.6 km = 484.9 km – the plane will fly to the west to get to Donetsk.
5) 484.9 km – 447.2 km = 37.7 km – the plane will not reach Donetsk.
Answer: the plane will not reach Donetsk 37.7 km.

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