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(60oN, 29oW) and Q(60oN, 31oE) 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 (60oN, 45oE) 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.
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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.
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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.
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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.
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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.
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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 ).
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Form 4 Mathematics
A ship leaves port p for port R though port Q.Q is 200 km on a bearing of 2200 from P.R is 420 km on the bearing of 1400 from from Q.
Answer
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.
aNSWER
Form 4 Mathematics
The position of two towns are (20 S,300 E) and 20S, 37.4 0E) calculate , to the nearest km, the shortest distance between the two towns.(take the radius ofthe earth to be 6370 km)
answer
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.
answers
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.
answer
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.
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Form 4 Mathematics
Point P (400S, 450E) and point Q (400S, 600W) are on the surface of the Earth.
Calculate the shortest distance along a circle of latitude between the two points.
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Form 4 Mathematics
An aero plane flies at an average speed of 500 knots due East from a point p (53.40e) 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
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