At the same time two planes depart from JFK international airport. One plane flies exactly in northern direction, while the other one flies exactly to the east. Both planes fly at the same speed and at the same height. Which plane is after one hour the most far away from JFK?

The shortest distance between two points on earth (if supposed that the earth is a perfect sphere) can be determined by imagining a circular disk which goes exactly through the middle of the earth and through those two points. The shortest distance between those to points is then the edge of this circular disk. If you're flying exactly to the north, you'll continously flying over the edge of such a imaginary circular disk. So at every moment, you have taken the shortest path to reach that point. If you're flying straight to the east, you're not flying around the edge of such a circular disk. Hence you're not taking the shortest route. Therefore, the plane which flies in the northeren direction is after one hour the most far away from JFK.

For the same reason, planes which go from the US to the UK always go via Canada and not in a straight line on the world map as you might probably have thought.