Final answer:
Using the arc length formula and given Earth's radius, we calculated the change in longitude as the aircraft traveled east from point P to Q. The longitude of Q is approximately 51°E.
Step-by-step explanation:
An aircraft flies from point P at coordinates (30° N, 20°E) to point Q, which is 3500 km due east of P. To solve for the longitude of point Q, we will use the formula for the length of the arc on the Earth's surface: arc length = (central angle in radians) * radius of the Earth. Since the aircraft is flying due east from point P, the latitude remains the same at 30° N and only the longitude changes.
First, convert the arc distance flown from kilometers to meters (since the Earth's radius is given in meters), and the central angle to radians:
Arc distance = 3500 km = 3500000 meters,
Earth's radius R = 6400 km = 6400000 meters.
Next, we calculate the angle in radians by the formula:
Angle in radians = Arc distance / Radius = 3500000 / 6400000 = 0.546875 radians.
Then, we convert radians to degrees:
Angle in degrees = (Angle in radians * (180/π)), where π ≈ 3.142,
Angle in degrees = 0.546875 * (180/3.142) ≈ 31.324 degrees E.
So, the longitude of Q can be found by adding this angle to the original longitude of P:
Longitude of Q = Longitude of P + Angle in degrees,
Longitude of Q = 20°E + 31.324°E ≈ 51°E (rounded to the nearest degree).
Therefore, the value of X, which represents the longitude of point Q, is approximately 51°E.