Question

One airplane flies 10 miles due south from its base, turns 90° and flies due west, then returns directly to base, which is now 13 miles away.

The second aircraft flies 10 miles due east from its base, turns 90° and flies due south, then _______.
a) Returns directly to base.
b) Turns 90° and flies due east.
c) Turns 180° and flies due west.
d) Turns 90° and flies due north.

Answer 1

The second aircraft, after flying 10 miles due east from its base, turns 90° and flies due south. It will then return directly to its base.

Step-by-step explanation:

The second aircraft, after flying 10 miles due east from its base, turns 90° and flies due south. To continue in the same pattern as the first aircraft, it should then return directly to base. This is because the second aircraft needs to complete a rectangular path, just like the first aircraft did.

Answer 2

The second aircraft should turn 90° and fly due north to return directly to its base after flying 10 miles due east and then due south, consistent with the symmetry to the flight path of the first airplane which turned and returned to base after its own maneuvers.

Step-by-step explanation:

The subject of this question is Mathematics, and it involves geometry and the principles of displacement. The question describes the different flight paths of two airplanes and asks what the second aircraft should do to return to its starting point. Given that one airplane flies 10 miles due south from its base, turns 90° and flies due west before returning directly to base, the second aircraft's movements should be symmetrical to the first, but in the perpendicular directions. As such, after flying 10 miles due east and turning 90° to fly due south, to return directly to its original starting point, the second aircraft should turn 90° and fly due north.