Theory question 113
Variation(a) P varies directly as Q and inversely as the square of R. If P = 1 when Q = 8 and R = 2, find the value of Q when P = 3 and R = 5.
(b) An aeroplane flies from town A(20°N, 60°E) to town B(20°N, 20°E). (i) If the journey takes 6 hours, calculate, correct to 3 significant figures, the average speed of the aeroplane. (ii) If it then flies due north from town B to town C, 420 km away, calculate, correct to the nearest degree, the latitude of town C. [Take radius of the earth = 6400 km and π = 3.142]
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(a) P = kQ/R2: 1 = 8k/4, so k = ½. Q = 2PR2 = 2 × 3 × 25 = 150.
(b)(i) Longitude difference = 40°. Distance = 40/360 × 2 × 3.142 × 6400 × cos 20° ≈ 4199 km.
Speed = 4199 ÷ 6 ≈ 700 km/h.
(ii) Along a meridian: 420 = θ/360 × 2 × 3.142 × 6400, so θ ≈ 3.76°.
Latitude of C ≈ 20° + 3.76° ≈ 24°N.
Along a parallel of latitude the radius is R cos(latitude); along a meridian it is R.