(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 = 3.142].
Explanation
(a) and . When P = 1, Q = 8, R = 2 When P = 3, R = 5, Q = ? . (b) Angular difference : 60° - 20° = 40° = = = (to 3 significant figures) (ii) Latitude of C : 20° + 3.76° = 23.76° Note that due North implies same longitude but different latitude.