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Form 4 Mathematics : Longitudes and Latitudes Topical Questions and Answers
A point Q is 2000 nm to the west of P
(
60
0
N
,
0
0
)
. Find the longitude of Q to the nearest degree.
(5m 6s)
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1.
A globe representing the earth has a radius 0.5m. Points A
(
0
0
,
10
0
W
)
, B
(
0
0
,
35
0
E
)
, P
(
60
0
N
,
110
0
E
)
and Q
(
60
0
N
,
120
0
W
)
are marked on the globe. (a) Find the length of the arc AB, leaving your answer in terms of
π
(b) If O is the centre of the latitude 600N, find the area of the minor sector OPQ.
2.
(a) Calculate the distance round the latitude
60
0
N
. (Take the radius of the earth, R=6370km and
π
=
22
7
) (b) An aeroplane flew due south from point A
(
60
0
N
,
45
0
E
)
, to a point B. The distance covered by the aeroplane was 8000km. Determine the position of B.
3.
The latitude and longitude of two stations A and B are
(
47
0
N
,
25
0
E
)
and
(
47
0
N
,
70
0
E
)
. Calculate the distance in nautical mile between A and B along latitude
47
0
N.
4.
A point Q is 2000 nm to the west of P
(
60
0
N
,
0
0
)
. Find the longitude of Q to the nearest degree.
5.
A and B are two points on the latitude
40
0
N
. The two points lie on the longitudes
20
0
W
and
100
0
E
respectively. Calculate the distance from A to B along a parallel of latitude. (Take
π
=
22
7
and R=6370km)
6.
An aeroplane flies from point A
(
1
0
15
′
S
,
37
0
E
)
to a point B directly North of A. The arc AB subtends an angle of
45
0
at the centre of the earth. From B, the aeroplane flies due west to point C on longitude
23
0
W
. (Take the value of
π
a
s
22
7
and radius of the earth as 6370km) (a) (i) Find the latitude of B (ii) Find the distance travelled by the aeroplane between B and C.
7.
The position of two towns A and B on the earth’s surface are
(
36
0
N
,
49
0
E
)
and
(
360
N
,
131
0
W
)
respectively. (a) Find the difference in Longitude between A and B. (b) Given that the radius of the earth is 6370km, calculate the distance between town A and town B. (c) Another town C is 840km east of town B and on the same latitude as towns A and B. Find the longitude of town C.
8.
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. (a) Calculate the distance between the two islands (i) In nautical miles (ii) In kilometers (b) Calculate the speed of the ship in kilometers per hour. (c) Find the position of the second island
9.
The position of two towns X and Y are given to the nearest degrees as
X
(
45
0
N
,
10
0
E
)
and Y
(
45
0
N
,
70
0
E
)
. Find (a) the difference in longitude (b) the distance between the two towns in (i) kilometers (take the radius of the earth as 6370 km) (ii) Nautical miles ( take 1 nautical mile to 1.85km) (c) the local time at X when local time at Y is 2.00pm
10.
A plane leaves an airport A
(
38.5
0
N
,
37.05
0
W
)
and flies due North to a point B on latitude 520N. (a) Find the distance covered by the plane (b) The plane then flies due East to a point C, 2400km from B. Determine the position of C.
11.
A plane flies at 200 knots left an airport A
(
30
0
S
,
31
0
E
)
and flew due North to an airport B
(
30
0
N
,
31
0
E
)
. (a) Calculate the distance covered by the plane, in nautical miles (b) After a 15 minutes stopover at B, the plane flew due West to an airport C
(
30
0
N
,
13
0
E
)
at the same speed. Calculate the total time taken to complete the journey from airport A to airport C,
12.
Two towns A and B lie on the same latitude in the northern hemisphere. When it is 8.00am at A, the time at B is 11.00am. (a) Given that the longitude of A is
15
0
E
, find the longitude of B. (b) A plane leaves A for B and takes
3
1
2
hours to arrive at B travelling along a parallel of latitude at 850km/h. Find: (i) The radius of the circle of latitude on which towns A and B lie.
13.
Two places P and Q are at
(
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.
14.
Two places A and B are on the same circle of latitude north of 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 mile. Find to the nearest degree, the latitude on which A and B lie.
15.
An aeroplane flies at an average speed of 500 knots due East from a point P
(
53.4
0
N
.40
0
E
)
to another point Q. It takes
2
1
4
hours to reach point Q. Calculate: (i) the distance in nautical miles it travelled (ii) the longitude of point Q to 2 decimal places.
16.
Point
(
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.
17.
The positions of three ports A, B and C
(
34
0
N
,
16
0
W
)
,
(
34
0
N
,
24
0
E
)
and
(
26
0
S
,
16
0
W
)
respectively. (a) Find the distance in nautical miles (i) Ports A and B to the nearest nautical miles. (ii) Ports A and C (b) A ship left port A on Monday at 1330h and sailed to port B at 40knots. Calculate: (i) The local time at port B when the ship left port A
18.
A point M
(
60
0
N
,
18
0
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
19.
A tourist took 1h 20 minutes to travel by an aircraft from town T
(
3
0
S
,
35
0
E
)
to town U
(
9
0
N
,
35
0
E
)
. (Take the radius of the earth to be 6370km and ??=22 7 (a) Find the average speed of the aircraft. (b) After staying at town U for 30minutes, the tourist took a second aircraft to town V
(
9
0
N
,
5
0
E
)
. The average speed of the second aircraft was 90% that of the first aircraft.
20.
The positions of the 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 of the earth to be 6370km)
21.
The shortest distance between two points A
(
40
0
N
,
20
0
W
)
and B
(
θ
0
S
,
20
0
W
)
on the surface of the earth is 8008 km. Given that the radius of the earth is 6370 km, determine the position of B. (take
π
=
22
7
).
22.
The position of two points P and Q, on the surface of the earth are
P
(
45
0
N
,
36
0
E
)
and
Q
(
45
0
N
,
71
0
E
)
. Calculate the distance, in nautical miles, between P and Q, correct to 1 decimal place.
23.
An aircraft took off from a point
P
(
65
0
S
,
76
0
W
)
and flew due North to a point Q. The distance between P and Q is 5400nm. Determine the position of Q.
24.
The position of two points C and D on the earths surface are
(
θ
0
N
,
10
0
E
)
and
(
θ
0
N
,
30
0
E
)
respectively. The distance between the two points is 600nm. Determine the latitude on which C and D lie.
25.
A ship left point
P
(
10
0
S
,
40
0
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 the radius of the earth to be 6370km) (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 11.00 a.m.
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