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# 27APR2020 Earth-as-a-Sphere (EXERCISE)

advertisement ```CHAPTER 16: EARTH AS A SPHERE
Important Notes:



The distance between two points on the surface of the Earth is the length of the arc connecting
the two places.
This distance (on the earth) is usually measured in nautical miles (n.m.)
The shortest distance from one point to another point on the surface of the earth is along the great
circle.
θ0 N
θ
Distance DE =  a 60 nautical miles


Distance FG =
b 60 nautical miles
Distance JK =
 c  60  cos
nautical miles
The distance along the longitude = the difference between two latitudes  60 n.m.
The distance along a parallel of latitude
= the difference between two the two longitudes  60  cos  0 n.m.
N
Example:
P●
00
600 N
C
O
●A
●
AB =
●B
PQ =
●X
AC =
Q●
1000 E
700S
S
Earth As A Sphere
800 E
1
 60  60 = 3600 n.m.
130  60 = 7800 n.m.
 20  60  cos 60 = 600 n.m.
16.1 The Distance Along The Surface of the Earth (Along The Meridian)
1. (a) Ex : Calculate the distance of PQ
2. (a) Ex : Calculate the distance of PQ
N
N
670 N
P
700 N
Q
450 N
220
Q
O
O
O0
P
R
S
S
The difference between two latitudes = 670 – 450
= 220
The distance of PQ
= 22  60’
= 1320 n.m
The difference between two latitude = 700 -00
= 700
The distance of PQ
= 70  60’
= 4200 n.m
b) Given the distance of QR is 6600 b.n. Find
the latitude of R.
b) Find the distance PQ
The difference between the two latitudes
P
=
720 N
6600
60
= 1100
230 S
The latitude of R = 1100 – 700
Q
= 400 S
Earth As A Sphere
2
3.
4.
N
N
700 N
Q
A
500 N
B
O0
P
C
R
S
S
(a) Calculate the distance AB
a) Given the distance PQ is 2700 n.m. and
P (0, 900W), find the latitude of Q
b) Given the distance of AC is 9000 nm, find
the latitude of C.
b) Given PQ = PR, find the latitude of R.
Earth As A Sphere
3
6. P(100 N, 800 E), Q and R are three points on
the earth surface. Q lies on to the north of P
and R lies on to the south of P.
5.
P
O
1100
Q
a) The distance of PQ along the meridian is
2700 nm. Find the latitude of Q.
00
R
(a) Given  POR = 1100, PQ = QR.
Find the distance of PQ.
b) The distance of PR along the meridian is
1920 nm. Find the latitude of R.
b) State the latitude of P and R.
Latitude of P =
Latitude of R =
Earth As A Sphere
4
16.2 The Distance on the Surface of the Earth (Along The Equator)
c) P (00, 700 W) , Q (00, 120 E)
1. Calculate the distance of PQ
(a)
P
0
45 W
Q
100 W
The difference between two latitudes = 450 – 100
= 350
The distance PQ
= 35  60
= 2100 n.m
d) P (00, 320 E) , Q (00, 400 W)
b) Find the distance PQ:
e) P (00, 70030’ E) , Q (00, 290 30’ W)
Q 00
P
230 W
Earth As A Sphere
230 E
5
a) Given P (00, 100 E) and R (00, 100 W),
calculate the distance from P to R.
U
2.
O
Q
R
P
800 W
a)
100 E
S
Calculate the distance of PQ
The difference between two longitudes
= 800 + 100
= 900
The distance of PQ
= 90  60’
= 5400 n.m
b)
b) The distance of PQ along the equator is
2400 nautical miles. Find the longitude of
Q.
Given PR = 3120 n.m
Find the longitude of R
The difference between longitudes P and R
=
3120
60
= 520
 Longitude of R = 100 + 520
=
620 E
3.
U
O
R
100 W
Earth As A Sphere
Q
P
S
100 E
6
U
4.
5.
O
R
Q
P
00
U
O
Q
P
100 E
S
a)
Calculate the distance PQ.
b)
Given PR =
1000 E
250 W
a)
1
PQ, find the longitude of R.
3
Earth As A Sphere
R
00
S
The distance of PQ along the equator is 900
nautical miles. Find the longitude of Q.
b) Given the distance of PR = 2PQ. Find the
longitude of R.
7
b)
6. Given P (00, 250 E), Q lies in the east of P and
R lies on the west of P.
Given PR =
1
PQ, calculate the distance
2
of QR.
a) The distance of PQ along the equator is
1920 nautical miles. Calculate the
longitude of Q.
16.3 The Distance Along The Surface of the Earth (Along The Common Parallel Of Latitude)
1. a) Calculate the distance of PQ.
b)
Q (100 S, 100 W)
Q
P(150 S, 300 E)
P(100 S, 00)
230 E
Q (150 S, 550 W)
The difference of two longitudes = 550+ 300
= 850
The distance of PQ
= 85  60’  kos150
= 4926.09 n.m
Earth As A Sphere
8
c)
P (500 N, 300 W), Q (500 N, 400 E)
2.
N
600 N
Q
P
R
700 W
200 W
a)
d)
P (400 S, 250 W), Q (400 S, 790 E)
S
Find the distance of PQ.
The difference between of P and Q
longitude = 700 - 200 = 500
 The distance of PQ
= 50  60  cos 600
= 1 500 n.m
b) Given PR = 4 200 nautical miles. Find the
longitude of R.
4 200 = the difference between two
longitude  60  cos 600
The difference between two longitude
e)
P (160 S, 100 30’ E), Q (160 S, 210 30’ W)
=
4200
= 1400
60 X cos 60
 find the longitude of R.
= 1400 - 200
= 1200 E
Earth As A Sphere
9
3.
4.
N
N
Q
700 N
P
Q
P
R
R
450 S
450 W
100 W
0
200 W
S
S
50 E
a) Find the distance of PQ.
a) Find the distance of PQ.
b) Given PR = 1200 nautical miles, find the
longitude of R.
b) Given PR = 2PQ, find the longitude of R.
Earth As A Sphere
10
6. Given P (750 N, 420 E), Q (750 N, 420 W)
and R lies in between PQ with PR = QR
5.
N
a) Find the position of R.
200
O
R
00
P
Q
S
300W
a) Given PQ = 1234 nautical miles. Find the
longitude of Q.
b) Find the distance of PR measured along the
common parallel latitude.
b) Given the longitude of R is 1000 W.
Find the distance of QR.
Earth As A Sphere
11
16.4
The shortest distance (is always the distance along the great circles)
Find the shortest distance between P and Q.
1.
2.
N
Q
P
N
700 N
P
500 N
Q
500 N
O
100 W
100 W
0
170 E
1700 E
S
S
 POQ = 1800 – (500 + 500)
= 800
Distance = 80  60
= 4800 n.m
 The shortest distance between P and Q
= 4800 n.m
N
3.
4.
N
400 N
P●
00
P
Q
●
●
250 W
●Q
400 S
300 E
S
S
Earth As A Sphere
12
Find the shortest distance between P and Q. (You are advised to sketch a diagram)
5. P (400 S, 1000 W), Q (400 S, 800 E)
7.
P (00, 1100 W), Q (00, 100 E)
Earth As A Sphere
6. P (100 S, 700 W), Q (350 S, 1100 E)
8. P (400 N, 500 W), Q (400 S, 1300 E)
13
Questions based on the examination format (Paper 2)
1. F (400 S, 720 E), G (400 S, 100 W), H and J are four points on the surface of the earth.
FH is the diameter of the earth and J is located at a distance of 3780 nautical miles due
north of F.
(a) State the position of H
[1marks]
(b) Calculate the latitude of J
[2 marks]
(c) Calculate the distance, in nautical miles from G eastwards to F, measured along
the common parallel of latitude.
[5 marks]
(d) An aeroplane took off from G and flew due east to F and then due north to J.
The average speed of the aeroplane for the whole flights is 500 knots, find
the time of flight.
[4 marks]
2.
P (00, 720 E), Q and R are three points on the surface of the earth. Q is due south of
P and QR is the diameter of the parallel of latitude 200 S.
N
O
Equator
Q
R
S
(a) Mark the position of P on the diagram above.
[1 mark]
(b) State the longitude of R
[2 marks]
(c) Calculate the shortest distance, in nautical miles, from Q to R, measured along the
surface of the earth.
[3 marks]
(d) An aeroplane took off from P and flew due south to Q and then due west to R.
The average speed of its flight is 560 knots. Calculate
(i) the total distance, in nautical miles, travelled by the aeroplane,
(ii) the total time, in hours taken by the aeroplane for the whole flight
[6 marks]
3. P (500 N, 800 E), Q (500 N, 100 W) and R are three points on the surface of the earth.
(a) Calculate the shortest distance, in nautical miles, from P to the North Pole
measured along the surface of the earth.
[3 marks
(b) Given that R is 3620 nautical miles due south of Q. Calculate the latitude of R
[4 marks]
Earth As A Sphere
14
(c ) An aeroplane took off from P at 0630 and flew westwards to Q along the
common parallel of latitude. The average speed of the flight is 350 knots.
Calculate the time of the aeroplane landed at Q.
[5 marks]
4.
F (00, x0 W), G (00, 600 E), H (460S, 600 E) and J (460S, 850 E) are four points on the
surface of the earth.
(a) Given that distance from F eastwards to G measured along the equator is 7920
nautical miles. Find the value of x.
[4 marks]
(b) An aeroplane took off from G and flew due south to H. Given that the whole
1
flight took 4
hours, calculate the average speed, in knots, of the aeroplane.
2
[4 marks]
(c) Another aeroplane took off from J at 1300, flew eastwards to H with an average
speed of 760 knots. Calculate its time of arrival at H.
[4 marks]
:
5. A (400 S, 300 W), B (400 S, 500 E) and C are three points on the earth‘s surface. AC is
the diameter of a parallel of latitude.
(a) State the longitude of C.
[1 marks]
(b) Calculate
(i) the distance, in nautical miles, from A eastwards to B, measured along
the common parallel of latitude.
(ii) the shortest distance, nautical miles, from A to C via South Pole.
[6 marks]
(c) An aeroplane took off from B and flew due north with an average speed of 570
knots. Calculate its latitude after flying 10 hours.
[5 marks]
6. P and Q are two points on the surface of the earth with latitudes 400 N. Longitudes of
P and Q are 200 E and 1600 W respectively.
(a) Calculate the distance, nautical miles, from P to Q, measured along the
common parallel of latitude.
[3 marks]
(b) An aeroplane took off from P and flew to Q at an average speed of 500 knots
via the North Pole. Calculate
(i)
the distance travelled by the aeroplane,
(ii)
the time taken of the whole flight
[4 marks]
(c) Another aeroplane took off from P and flew due west to Q half an hour after the
first aeroplane took off. Given that both of the aeroplanes reach Q at the same
time, calculate the average speed, in knots, of the second aeroplane.
[5 marks]
Earth As A Sphere
15
7.
N
C
D
00
O
A
B
S
In the diagram above, positions of A, B, C and D are  30S , 20W  ,
30S , 40E  ,  60N , 40E  and  60N , 20W  respectively.
(a) Calculate the shortest distance, in nautical miles,
(i) between A and B as measured along the common parallel of latitude,
(ii) between B and C as measured along the meridian.
[7 marks]
(b ) An aeroplane X took off from B and flew due east to A with an average
speed of 400 knots. At the same time, another aeroplane Y took off from D
and flew due south to A with an average speed of 600 knots. Find the
distance of aeroplane Y from A when aeroplane X reached A.
[5 marks]
8. P, Q and R are three points on the surface of the earth. PQ is the diameter of the 50N
parallel of latitude and PR is the diameter of the earth. The longitude of R is 75E.
a) Find
i) the latitude of R
ii) the longitude of P
b). Find the distance, in nautical miles, from P due east to Q measured along the
common parallel of latitude.
c) An aeroplane flew from P towards Q passing through the North Pole. The
aeroplane started from P at 0900 hours and arrived at Q at 1530 hours on the
same day. Find the average speed, in knots, of the aeroplane.
[50oS, 105oW; 6942 nm; 738.5 knots]
Earth As A Sphere
16
9. Points A  43S ,78W  , B  43S ,14E  , C and D are four points on the surface of the
earth. Point C lies to the north of A and AD is the diameter of the earth.
a)
State the location of D
b)
Given that the distance between A and C, measured along the meridian, is 4020
nautical miles, find the latitude of C.
c)
Find the distance, in nautical miles, from B due west to A, measured along the
common parallel of latitude.
d) An airplane took off from B at 0700 hours and flew due west to A along the
common parallel of latitude, then due north to C. If the airplane reached C at 1924
hours, find the average speed for the whole flight.
[(43oN, 102oE); 24oN; 4037 nm; 650 knots]
10.
E  50S ,63E  , F, G and H are four points on the surface of the earth. E, F and G lie of
the common parallel of latitude, such that EF is the diameter of that common parallel of
latitude. The longitude of G is 47oW and H lies to the north of G.
d)
Find the longitude of F.
e)
An aeroplane took off from E and flew due west to G. Then, the aeroplane
flew due north to H which is 5100 nautical miles from G. The average speed of
the aeroplane from E to H is 680 knot.
Calculate
i) the latitude of H
ii) the distance, in nautical miles, from E to G
iii) the time, in hours, taken for the flight from E to H.
[117oW; 350N; 4242.48 nm; 13.74 hours]
11. K, L and M are three points on the surface of the earth on the parallel of latitude 56S .
The longitude of K is 60E whereas the longitude of L is 10E . Given KM is the
diameter of the parallel of latitude 56S .
Find
a) the longitude of M.
b) the shortest distance, in nautical miles, between K and M measured along the
surface of the earth.
c) the distance, in nautical miles, from K to L measured along the parallel of
latitude.
d) the duration of the flight from L to the North Pole, along the shortest distance by
an aeroplane at an average speed of 700 knots.
[120oW; 4080 nm; 1678 nm; 12 hours 31 minutes]
12. A  71 N ,18E  and B are two points on the earth’s surface such that AB is a diameter of a
parallel of latitude.
a) Find the longitude of B
b) AC is a diameter of the earth. On a diagram, mark the positions of A, B and C.
Hence, state the latitude and longitude of C.
c) Calculate the shortest distance, in nautical miles, from B to the North Pole.
Earth As A Sphere
17
d) An aeroplane took off from A and flew due west along its parallel of latitude at
an average speed of 540 knots. The aeroplane took 6 hours to reach a point X.
Calculate
i. the distance, in nautical miles, from A to X,
ii. the longitude of X.
[162oN; C (71oS, 162oW); 1140 nm; 3240 nm, 147o52’W]
13. K  50S ,80E  , L and M are three points on the earth’s surface. KL is a diameter of
the parallel of latitude 50S. M is 4860 nautical miles due north of K.
a) State the longitude of L.
b) Find the latitude of M.
c) Calculate the distance, in nautical miles, from K to L measured along the parallel
of latitude.
d) An aeroplane flew from L to K using the shortest route measured along the
earth’s surface and then flew due north to M. Given that the average speed for
the whole flight is 630 knots, calculate the total time of flight.
[100oW; 31oN; 6942.1 nm; 15 hours 20 minutes]
14. A  0, 24E  and B are two points on the equator while C and D are two points on th
common parallel of latitude. C and D lie due north of A and B respectively.
a) Given that the distance from A to C, measured along the meridian, is 3360
nautical miles, find the latitude of C.
b) Given that the longitude of D is 42oW, calculate the distance from C due west to
D, measured along the common parallel of latitude.
c) An aeroplane took off from C and flew along the shortest route to D, then, due
south to B. If the average speed of the aeroplane for the whole flight was 550
knot, calculate
i)
the total distance covered
ii)
the time taken for the whole flight
[56oN; 2214.4 nm; 7440 nm; 13 hours 32 minutes]
15.
A  30S , 40E  , B  30S ,80W  and C are three points on the surface of the earth
and AC is the diameter of the common parallel of latitude.
a) (i)
Find the longitude of C
(ii) Find the difference, in nautical miles, between the distance fro A to C via
the North Pole and the distance from A to C via the South Pole.
(iii) Calculate the distance, in nautical miles, from A due west to B, measured
along the common parallel of latitude.
b) Calculate the latitude of a point, D, which lies 4110 nautical miles due
north of B.
[140oW; 7200 nm; 6235.4 nm; 38o30’N]
Earth As A Sphere
18
16.
17.
P, Q, R and V are four points on the Earth’s surface. The longitude of Q and R are
50oW and 110oW respectively. Q and R are due east of P on the latitude 58oN such
that PQ = QR. Point V which is on the latitude 76oN is due north of R.
a) Find the longitude of P.
b) Calculate, in nautical miles,
i)
the distance, measured along their common latitude, from Q due east to R.
ii)
the shortest distance, measured along the earth’s surface, from R due
north to V
c) An aeroplane flying at an average speed of 600 knots, flew due east from Q to R
and then flew due north from R to V. Calculate to the nearest hour, the total time
taken for the whole journey.
[10oW; 1908 nm; 1080 nm; 5 hours]
Two aeroplanes took off from an airport at A  40N , 20E  and flew to their
destinations at an average speed of 600 knots. The first aeroplane flew due west and
1
arrived at B after flying of the circumference of the parallel of latitude 40oN. The
5
second aeroplane used the shortest route to arrive at C  20S ,160W  .
a)
Find the longitude of B.
b)
D is another point on the earth’s surface such that CD is a diameter of the
earth. Find the latitude of D.
c)
Calculate
i) the distance each aeroplane travelled in nautical miles.
ii) the difference in time the two aeroplanes took for their respective flights.
[52oW; 20ON; 3309.3 nm and 9600 nm; 10 hours 29 minutes]
Earth As A Sphere
19
Past Year SPM Questions
Paper 2
1. November 2003 (Paper 2, Q 16)
P (610 N, 100 E) and Q are two points on the surface of the earth such that PQ is the diameter
of a parallel of latitude.
(a) Find the longitude of Q
[1 mark]
(b) PR is the diameter of the earth. On the diagram below, mark the positions of Q and R.
Hence, state the position of R.
N
[4 marks]
P
Equator
S
(c ) Calculate the shortest distance, in nautical miles, from Q to the North Pole. [2 marks]
(d) An aeroplane took off from P flew due west along its parallel of latitude with an average
speed of 500 knots. The aeroplane took 9 hours to reach a point M.
Calculate
(i) the distance in nautical miles, from P to M
(ii) the longitude of M
[5 marks]
2. July 2004 (Paper 2, Q 16)
P  35S ,58W  , Q  35S , 24E  , R and V are four points on the surface of the earth. PR is a
diameter of the earth and V is located at a distance of 3060 nautical miles due north of Q.
(a) State the longitude of R.
[2 marks]
(b) Calculate the latitude of V.
[3 marks]
(c) Calculate the distance, in nautical miles, from P eastwards to Q, measured along the
common parallel of latitude.
[3 marks]
(d) An aeroplane took off from P at 0800 hours and flew due east to Q and then due north to
V. Given that its average speed for the whole flight is 600 knots, at what time did the
aeroplane arrive at V?
[4 marks]
Earth As A Sphere
20
3. November 2004 (Paper 2, Q16)
P (600 S, 700 E), Q and R are three points on the surface of the earth. PQ is the diameter of the
parallel of latitude 600 S. R lies 4 800 nautical miles due north of P.
(a) State the longitude of Q.
[2 marks]
(b) Find the latitude of R.
[3 marks]
(c) Calculate the distance, in nautical miles, from P to Q measured along the parallel latitude.
[3 marks]
(d) An aeroplane took off from Q and flew towards P using the shortest distance, as measured
along the surface of the earth, and then flew due north to R.
Given that its average speed for the whole flight was 560 knots, calculate the total time
taken for the flight.
[4 marks]
4. July 2005 (Paper 2, Q16)
F  0,50W  , G and H are three points on the surface of the earth. G is due north of F and
GH is the diameter of the parallel of latitude 30oN.
a.
On Diagram 10 in the answer space, mark the position of F.
[1 mark]
b.
State the position of H.
c.
d.
[2 marks]
Calculate the shortest distance, in nautical miles, from G to H measured along the
surface of the earth.
[3 marks]
An aeroplane took off from F and flew due north to G and then due east to H. The
average speed of the aeroplane is 500 knots.
Calculate
i)
the total distance, in nautical miles, travelled by the aeroplanes
ii)
the total time, in hours, taken by the aeroplane for the whole flight.
[6 marks]
N
H
G
Equator
DIAGRAM 10
S
Earth As A Sphere
21
5. November 2005 (Paper 2, Q 16)
The table below shows the latitudes and longitudes of four points J, K, L and M, on the
surface of the earth.
Point
Latitude
Longitude
J
20N
25E
K
xS
25E
L
y W
20S
M
30S
y W
(a) P is a point on the surface of the earth such that JP is the diameter of the earth.
State the position of P.
[2 marks]
(b) Calculate
(i) the value of x, if the distance from J to K measured along the meridian is 4200
nautical miles.
(ii) the value of y, is the distance from J due west to L measured along the common
parallel of latitude is 3270 nautical miles.
[7 marks]
(c) An aeroplane took off from J and flew due west to L along the common parallel of latitude
and then due south to M. If the average speed for the whole flight is 600 knots, calculate
the time taken for the whole flight.
[3 marks]
6. July 2006 (Paper 2, Q16)
Diagram 8 shows the point P  47 N ,12W  and the point Q on the surface of the earth. The
point C is the centre of the common parallels of latitude of P and Q.
N
C
50O
P
Q
DIAGRAM 8
S
(a)
(b)
State the position of Q
[3 marks]
R is a point on the surface of the earth. It is given that R is situated at a distance
of 2400 nautical miles due south of P, measured along the meridian.
Find the latitude of R.
[4 marks]
Earth As A Sphere
22
(c)
(d)
Calculate the distance, in nautical miles, from P due east to Q, measured along
the common parallels of latitude.
[3 marks]
An aeroplane took off from Q and flew due west to P along the common parallel
of latitude. Then, it flew due south, along the meridian, to R.
1
It is given that the total time taken for the flight is 7 hours.
2
Calculate the average speed, in knots, of the aeroplane for the whole flight.
[2 marks]
7. November 2006 (Paper 2, Q16)
Diagram 9 shows four points P, Q, R and X, on the surface of the earth. P lies on the longitude
of 80W . QR is the diameter of the parallel of latitude of 50 N . X lies 5820 nautical miles due
south of P.
N
R
P
Q 35O
50O
O
X
DIAGRAM 9
S
(a)
(b)
(c)
(d)
Find the position of R.
[3 marks]
Calculate the shortest distance, in nautical miles, from Q to R, measured along
the surface of the earth.
[2 marks]
Find the latitude of X.
[3 marks]
An aeroplane took off from P and flew due west to R along the parallel of latitude
with an average speed of 600 knots.
Calculate the time, in hours, taken for the flight.
[4 marks]
Earth As A Sphere
23
8 SPM Jul 2007. Q14
P (250 N , 600 E ), Q and R are three points on the surface of the earth.
PR is the diameter of the earth.
(a)
State the longitude of R.
[2 marks]
(b) PQ is the diameter of the parallel of latitude 250 N .
(i) State the position of Q .
(ii) Calculate the shortest distance, in nautical mile, from P to Q
measured along the surface of the earth.
(c)
[4 marks]
An aeroplane took off from P and flew due west to Q along the
common parallel of latitude and then flew due south to R.
Calculate
(i) the distance, in nautical miles, from P to Q measured along
the common parallel of latitude.
(ii) the time taken, in hours, for the whole flight if the average speed
of the whole flight is 650 knots.
Earth As A Sphere
24
[6 marks]
9 SPM, Nov 2007 Q14
P (650 N , 400 W ), Q ( 650 N, 600 E ), R and V are four points on the
surface of the earth. PR is the diameter of the parallel of latitude 650 N.
(a)
(i) State the longitude of R.
(ii) Calculate the shortest distance, in nautical mile, from P to R
measured along the surface of the earth.
[4 marks]
(b) V lies south of Q and the distance VQ measured along the surface
of the earth is 4500 nautical mile.
Calculate the latitude of V .
(c)
[3 marks]
An aeroplane took off from P and flew due east to Q and then flew
due south to V. The average speed for the whole flight was 550 knots.
Calculate
(i) the distance, in nautical miles, taken by the aeroplane from P
to Q measured along the common parallel of latitude,
(ii) the total time taken, in hours, taken for the whole flight .
[5 marks]
10 SPM Jun 2008. Q16
P (250 N , 1200 E ), Q , R , M and V are five points on the surface of the
earth. PQ is the diameter of the earth. R lies 2100 nautical miles along the
common parallel of latitude due west of P.
(a)
State the location of Q.
[2 marks]
(b) Fine the longitude of R.
[4 marks]
(c)
PM is the diameter of the parallel latitude 50 N.
Calculate the shortest distance, in nautical mile, from P to M ,
Measured along the surface of the earth.
[2 marks]
(d)
An aeroplane took off from P , flew due west to R , along the
common parallel of latitude. Then it flew due south to V which
lies due east of Q. It is given that the average speed of the whole
flight is 560 knots.
Calculate the total time taken for the whole flight.
[4 marks]
Earth As A Sphere
25
11 SPM Nov 2008, Q16
P (53 N , 84 W ), Q (53 N, 25 W ) , R and V are four points on the
surface of the earth.
PR is the diameter of the parallel of latitude of 53 N.
(a)
State the location of R.
[3 marks]
(b) Calculate the shortest distance, in nautical mile, from P to R
measured along the surface of the earth.
[2 marks]
(c)
Calculate the distance, in nautical mile, from P due east to
measured along the common parallel of latitude.
(d)
An aeroplane took off from Q and flew due south to V . The
average speed of the flight was 420 knots and the time taken
[3 marks]
was 6
1
hours .
2
Calculate
(i) the distance, in nautical mile, from Q to V measured along
the meridian ,
(ii) the latitude of V .
[4 marks]
Earth As A Sphere
26
ANSWERS
Past Year SPM Questions
1
Nov 2003
(a)
2
110 W
(b) 20 N
P(20 S , 155 W)
R(50 N , 135 E)
(c) 5400
(d) 15 hours
(b) x = 50 , y = 33
(c) 10.45 hours
(b) 4800
(c)
47 S
(d) 9.32 hours
Jun 2007
(a) (i) 120 W
(c) (i) 9788 n.m
6
(d) (i) 4500 (ii) 147.7  W
Nov 2006
(a)
5
(c) 1740
Nov 2005
(a)
4
(b) 61 S , 170 W
Nov 2004
(a)
3
170 W
(b) (i) Q (25 N , 120 W) (ii)
(ii)
7800 n.m
19.67 hours
Nov 2007
(a) (i) 140 E , (ii) 3000 n.m
(b) 10 S
(c)
2535.71n.m
(d)
12.79 hours
7 Jun 2008
(a) Q(50 S , 60 W )
8
(b) 65.55 E
(c) 4800 n.m
(d) 14.46 hours
Nov 2008
(a) (53 N, 96 E )
Earth As A Sphere
(b) 4440
(c) 2130.4 n.m
27
(d) (i) 2730 n.m
(ii) 7.5  N
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