The Earth, and everything on it rotates counterclockwise, if viewed from space above the north pole. That means everything on it is also rotating. We don$$t feel the rotation because we don$$t have any immediate reference points. If we were in a soundproof car moving at a constant speed with the windows blacked out, we wouldn$$t know we were moving, because we have no reference. The only reference we have the are the stars, but they "move" so slow they are of little immediate use, with the exception of the sun. But as we all know, many people thought the sun moved around the Earth rather than vice versa. Because of Earth$$s rotation, atmospheric molecules move as well, but they are lighter, and thus freer than we are to move; this gives rise to weather patterns and phenomena such as jet streams. Jet streams are high altitude air currents that often arise between the troposphere and stratosphere $--$ where jet airplanes often fly. The jet streams flow in the direction of Earth$$s rotation, that is$,$ to the East. This is why it takes less time to travel to Europe from the US$,$ than vice versa or east across the US versus west.Consider a plane travelling from Chicago, Il to Rome, Italy at a speed of $800.$ km$/$h relative to the air $($airspeed$).$ In perfectly still air, the plane$$s airspeed is equal to its ground speed: the speed it would have on the ground. If the plane is flying in a parallel $100.$ km$/$h jet stream for $7,700.$ km $($the majority$)$ of its trip in air kilometers $($because the plane must fly farther at higher altitudes$),$ how long $($in hours$)$ would the the trip take?

Correct answer:

$8\mathrm{.}56$ hr

If the plane flies back under the same conditions, how long would the trip take?

Correct answer:

$11\mathrm{.}0$ hr

If the jet stream is angled at $30\mathrm{.}0$ degrees north of the plane$$s fuselage from Rome to Chicago, how long would the trip take?

Correct answer:

$10\mathrm{.}8$ hr

By what angle would the pilot need to correct the aircraft to maintain course? Hint: You can calculate this either with vectors, or geometry.

Incorrect answer:

$4\mathrm{.}58$ degrees

If the pilot did not correct the plane$$s trajectory for the partial crosswind, how far off course would the plane be if it travelled for $7700$ km$?$

Incorrect answer:

$540\mathrm{.}0$