An aeroplane flies from point P (30° N, 40° W) to point Q due east on the same latitude. The distance PQ is 4500 km. Find the longitude of Q.

Welcome back Ewurade — missed you this week. Step 1: Identify the given information and relevant formulas. The aeroplane flies from point P (30^ N, 40^ W) to point Q due east on the same latitude. The distance PQ is 4500 km. We need to find the longitude of Q. The latitude of both P and Q is = 30^ N. The radius of the Earth is approximately R = 6371 km. The formula for the distance (D) along a parallel of latitude is given by: D = R () · _rad where R is the Earth's radius, is the latitude, and _rad is the difference in longitude in radians. To convert _rad to degrees, we use _deg = _rad × (180^)/(). So, the distance formula can also be written as: D = _deg360^ × 2 R () Step 2: Calculate the radius of the parallel of latitude (r). The radius of the parallel of latitude at 30^ N is r = R (). r = 6371 km × (30^) r = 6371 km × sqrt(3)2 r ≈ 6371 km × 0.866025 r ≈ 5520.06 km Step 3: Calculate the difference in longitude (_deg). Using the distance formula D = _deg360^ × 2 r: 4500 km = _deg360^ × 2 × 5520.06 km Rearrange to solve for _deg: _deg = (4500 × 360^)/(2 × 5520.06) _deg = (1620000)/(34684.9) _deg ≈ 46.70^ Step 4: Determine the longitude of Q. Point P is at 40^ W. Since the aeroplane flies due east, the longitude increases (moves towards the east). We can represent west longitudes as negative values. Longitude of Q = Longitude of P + _deg Longitude of Q = -40^ + 46.70^ Longitude of Q = 6.70^ E Step 5: Round the longitude of Q to the nearest degree. Rounding 6.70^ E to the nearest degree gives 7^ E. The longitude of Q is 7^ E. Send me the next one 📸