Theory question 111
Latitude and Longitude(a) P and Q are points on the parallel of latitude 68.7°S, their longitude being 124°W and 56°E respectively. What is their distance apart measured along the parallel of latitude. [Take R = 6400 km, π = 3.142]. (Give your answers to 3 significant figures). (b) A bag contains four red, three white and five green balls (i) If one ball is picked at random, what is the probability that it is not green? (ii) If two balls are picked at random without replacement, what is the probability that one is red and the other white?
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(a) Longitude difference = 124° + 56° = 180° (one west, one east).
Radius of the parallel r = R cos 68.7°.
Distance = 180/360 × 2πR cos 68.7° = 3.142 × 6400 × 0.3633 ≈ 7305 km ≈ 7300 km (3 s.f.).
(b) Total = 4 + 3 + 5 = 12 balls.
(i) P(not green) = 1 − 5/12 = 7/12.
(ii) P(red then white) + P(white then red) = 4/12 × 3/11 + 3/12 × 4/11 = 1/11 + 1/11 = 2/11.
Along a parallel of latitude, distance = (longitude difference/360°) × 2πR cos(latitude).