(a) A and B are two points on earthâ€™s surface and on latitude 40^{0} N. The two points are on the longitude 50^{0}W and 130^{0}E respectively. Calculate the distance from A to B along a parallel of latitude in kilometers. (2mks)(b) The shortest distance from A to B along a great circle in kilometres (Take p = ^{22}/_{7} and radius of the earth = 6370km) (2mks)LONGITUDES AND LATITUDES  Distance between two points along the small and great circles in nautical miles and kilometres.  FORM 4 LEVEL  PAPER 2 QUESTIONS  SECTION B(a) (i) Taking the radius of the earth, R= 6370km and π = 22/7, calculate the shortest distance between the two cities P(60^{o}N, 29^{o}W) and Q(60^{o}N, 31^{o}E) along the parallel of latitude. (3mks)(ii) If it is 1200hrs at P, what is the local time at Q. (3mks)(b) An aeroplane flew due south from a point A (60^{o}N, 45^{o}E) to a point B. the distance covered by the aeroplane was 8000km. determine the position of B. (4mks)
Form 4 Mathematics
A ship left point P(10°S, 40°E) and sailed due East for 90 hours at an average speed of 24 knots to a point R.(Take 1 nautical mile (nm) to be 1.853 km and radius of the earth to be 6370 km)
(a) Calculate the distance between P and R in: (i) nm; (ii) km. (b) Determine the position of point R. (c) Find the local time, to the nearest minute, at point R when the time at P is 11:00a.m. Form 4 Mathematics
The position of two points C and D on the earth’s surface are (θ°N, l0°E) and (θ°N, 30°E)
respectively. The distance between the two points is 600 nm. Determine the latitude on which C and D lie. Form 4 Mathematics
An aircraft took off from a point P (65° S, 76° W) and flew due North to a point Q. The distance between P and Q is 5400 nm.
Determine the position of Q. Form 4 Mathematics
A tourist took 1 hour 20 minutes to travel by an aircraft from town T(3°S, 35°E) to town U(9°N, 35°E, ). (Take the radius of the earth to be 6370km and π = 22/7)
(a) Find the average speed of the aircraft. (a) After staying at town U for 30 minutes, the tourist took a second aircraft to town V(9°N, 5°E), The average speed of the second aircraft was 90% that of the first aircraft Determine the time, to the nearest minute, the aircraft took to travel from U to V. (c) When the journey started at town T, the local time was 0700h. Find the local time at V when the tourist arrived. Form 4 Mathematics
The positions of two points P and Q, on the surface of the earth are P(45 °N, 36°E) and Q(45 °N, 71°E). Calculate the distance, in nautical miles, between P and Q, correct to 1 decimal place.
Form 4 Mathematics
The shortest distance between two points A (40°N, 20°W) and B (0°S, 20°W) on the surface of y the earth is 8008km. Given that the radius of the earth is 6370km,
determine the position of B. (Take n = 22/7 ). Form 4 Mathematics
A ship leaves port p for port R though port Q.Q is 200 km on a bearing of 220^{0} from P.R is 420 km on the bearing of 140^{0} from from Q.
Form 4 Mathematics
Two towns A and B lie on the same latitude in the northern hemisphere. When its 8am at A, the time at B is 11.00am.
Form 4 Mathematics
The position of two towns are (2^{0} S,30^{0} E) and 2^{0}S, 37.4 ^{0}E) calculate , to the nearest km, the shortest distance between the two towns.(take the radius ofthe earth to be 6370 km)
Form 4 Mathematics
A tourist took 1 h 20 minutes to travel by an aircraft from town T(3°S, 35°E) to town U(9°N, 35°E). (Take the radius of the earth to be 6370km and π =22/7
(a) Find the average speed of the aircraft. (b) After staying at town U for 30 minutes, the tourist took a second aircraft to town V(9°N, 5°E). The average speed of the second aircraft was 90% that of the first aircraft. Determine the time, to the nearest minute, the aircraft took to travel from U to V (c) When the journey started at town T, the local time was 0700h. Find the local time at V when the tourist arrived. Form 4 Mathematics
A point M (60°N, 18°E) is on the surface of the earth. Another point N is situated at a distance of 630 nautical miles east of M.
Find: (a) the longitude difference between M and N; (b) The position of N. Form 4 Mathematics
The positions of three ports A, B and C are (34°N, 16°W), (34°N. 24°E) and (26°S, 16°W) respectively.
(a) Find the distance in nautical miles between: (i) Ports A and B to the nearest nautical miles; (ii) Ports A and C. (b) A ship left Port A on Monday at 1330 h and sailed to Port B at 40 knots. Calculate: (i) the local time at Port B when the ship left Port A; (ii) the day and the time the ship arrived at port B. Form 4 Mathematics
Point P (40^{0}S, 45^{0}E) and point Q (40^{0}S, 60^{0}W) are on the surface of the Earth.
Calculate the shortest distance along a circle of latitude between the two points. Form 4 Mathematics
An aero plane flies at an average speed of 500 knots due East from a point p (53.4^{0}e) to another point Q. It takes 2 ¼ hours to reach point Q. Calculate:
(i) The distance in nautical miles it traveled; (ii) The longitude of point Q to 2 decimal places Form 4 Mathematics
Two places A and B are on the same circle of latitude north of the equator. The longitude of A is 118^{0}W and the longitude of B is 133^{0}E. The shorter distance between A and B measured along the circle of latitude is 5422 nautical miles.Find, to the nearest degree, the latitude on which A and B lie
Form 4 Mathematics
Two places P and Q are at ( 36^{0}N, 125^{0}W) and 36^{0}N, 125^{0}W) and 36^{0} N, 125^{0}W) and 36^{0} N, 55^{0}E) respectively. Calculate the distance in nautical miles between P and Q measured along the great circle through the North pole.
Form 4 Mathematics
A plane leaves an airport A (38.5^{0}, 37.05^{0}W) and flies dues North to a point B on latitude 52^{0}N.
Take the value Π of as ^{22} ⁄ _{7} and radius of the earth as 6370 km Related Questions on Longitudes and LatitudesFree 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2
â€‹A river is flowing at uniform speed of 6 km/ h. A canoeist who can paddle at 10 km/h through still water wishes to go straight across the river.
Find the direction, relative to the bank in which he should steer. The position of two towns X and Y are given to the nearest degree as X (45^{0}N, 10^{0}W) and Y ( 45^{0}N, 70^{0}W)
â€‹Find
A ship leaves an island ( 5^{0}N, 45^{0}E) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots.
(take 1 nautical mile to be 1.853 Km and the radius of the earth to be 6370 Km) 
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