Theory question 112
Latitude and Longitude(a) Two points X(32°N, 47°W) and Y(32°N, 25°E), are on the earth's surface. If it takes an aeroplane 11 hours to fly from X to Y along the parallel of latitude, calculate its speed, correct to the nearest kilometre per hour (Take the radius of the earth = 6400km and π = 22/7).
(b) Two observers P and Q, 15 metres apart observe a kite (K) in the same vertical plane and from the same side of the kite. The angles of elevation of the kite from P and Q 35° and 45° respectively. Find the height of the kite to the nearest metre.
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(a) Difference in longitude = 47° + 25° = 72°
Distance = 72/360 × 2 × 22/7 × 6400 × cos 32° ≈ 8045.7 × 0.8480 ≈ 6823 km
Speed = 6823 ÷ 11 ≈ 620 km/h
(b) Let height = h. From Q (45°), horizontal distance = h; from P, distance = h + 15
tan 35° = h/(h + 15): 0.7002(h + 15) = h
0.2998h = 10.50, h ≈ 35 m
Along a parallel of latitude the radius is R cos(latitude).