16 earth as a sphere

8/12/2019 16 Earth as a Sphere

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Earth as a sphere:

(For the questions below you are strongly advised to sketch a diagram)

1. Given P(70oN, 35oW), Q and R are three points on the surface of the earth. PQ is the

diaeter of the earth !hi"e PR is the diaeter of the coon para""e" of "atitude. #tate the "ocation of

(a) Q, ($) R.

%. Given &(1'o#, o*), + and are three points on the surface of the earth such that

&+ $e the diaeter of the earth and & $e the diaeter of the coon para""e"

of "atitude.

#tate the "ocation of (a) +, ($) .

3. -(0oN, 0o*), G and are three points on the surface of the earth.

(a) G is 0

o

due east of -. #tate the position of G. ($) is '5odue south of -. #tate the position of .

. /(%0oN, 35o*), &, + and are four points on the surface of the earth.

(a) f & is 'odue east of /, state the position of &.

($) f + is 0odue !est of /, state the position of +. (c) f is 75odue south of /, state the position of .

5. Given points P(70oN, 0oW), Q(30oN, 0oW) and R(50o#, 0oW)

-ind the shortest distance, in nautica" i"es,easured a"on the surface of the earth (a) fro P to Q, ($) fro P to R.

'. -ind the shortest distance,in nautica" i"es, fro 2(50oN, 110oW) to (50oN, 70o*) via the north po"e.

7. -ind the shortest distance,in nautica" i"es, fro 4(%0o#, 5oW) to -(50o#, 135o*) easured a"on the surface of the earth.

. he shortest distance fro 6upo to the North Po"e is %310 nautica" i"es. -ind the

"atitude of 6upo.

. P(0oN, 5o*) and Q are t!o points on the earth8s surface. f Q is 500 nautica"

i"es due south of P, find the "atitude of Q.

10.&(5o#, 7o*) and +('3o#, 7o*) are t!o points on the surface of the earth.a"cu"ate

the distance, in nautica" i"es, $et!een the t!o points easured a"on the eridian.

11.P and Q are t!o points on the e9uator. Q is due east of P and the "onitude of Q is

0o*. f the shortest distance fro P to Q is 3%0 nautica" i"es, find the "onitude

of P.


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1%. -ind the distance fro P('0o#,50oW) to Q('0o#,130o*)

(a) a"on the shortest distance on the surface of the earth,

($) a"on the coon para""e" of "atitude.

13.Given P('0oN,30oW), Q('0oN, 70oW) and R('0oN, 0o*) are points on the surface of

the earth. -ind the distance a"on the coon para""e" of "atitude (a) fro P to Q,

($) fro P to R.

1. 4(70oN, 100oW) and - are t!o points on the surface of the earth. f the shortest

distance fro 4 to - via the North Po"e is 5100 nautica" i"es ,find the "atitude of -.

15. f an averae speed of an o$:ect is 50 ;nots !ith the tie ta;en is hours ,find the distance it trave"s.

1'. he distance fro & to + a"on the shortest distance is 500 nautica" i"es.-ind the

tie ta;en of an aerop"ane fro & to + if it f"ies !ith a speed of 00 ;nots.

17. Given /(0o#, 10oW), &(30oN, 10oW) and +(0o#, 70o*). (a) 2n aerop"ane < f"ies fro / due north to & !ith an averae speed of 700 ;nots.

-ind the tie ta;en.

($) 2n aerop"ane = f"ies fro / due east to + in a period of hours. -ind the averae speed.

1. 2n aerop"ane f"ies fro 2(0oN, 70oW) due east to (0oN, 10oW) and proceed to

f"> due south to 4(5oN, 10oW). f the averae speed of the aerop"ane is 500 ;nots, find the tie ta;en of the f">in.

1. P(?oN,70oW) and Q(%5oN,70oW) are t!o points on the surface of the earth. f the shortest distance fro P to Q easured a"on the surface of the earth is 00

nautica" i"es , find the va"ue of ?.

%0. is the idpoint $et!een & and + easured a"on the coon para""e" of "atitude.

Given & is (%0oN,15oW) and + is (%0oN,75o*),find the "onitude of .


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#ap"e 1@

/(0oN, 110o*), &, +, P and Q are five points on the surface of the earth. /& is the

diaeter of the earth. + "ies %100 nautica" i"es due !est of / a"on the coon para""e"of "atitude.

J(40o

N, 110o

E), K, L, P dan Q adalah lima titik di permukaan bumi. JK ialah diameterbumi. L terletak 2100 batu nautika ke barat J di epan!an" elarian latitud epun#a.

(a) #tate the "ocation of &. A3 ar;sB N#atakan kedudukan ba"i K. $%

markah&

($) -ind the "onitude of +. A ar;sB 'ari lon"itud ba"i L. $4 markah&

(c) /P is the diaeter of the para""e" "atitude of 0oN.

a"cu"ate the shortest distance, in nautica" i"e,fro / to P,easured a"on thesurface of the earth. A3 ar;sB

JP ialah diameter elarian latitude 40o itun" !arak terpendek,dalam batu nautika,dari J ke P,di ukur epan!an"

permukaan

bumi. $% markah&

(d) Q "ies 100 nautica" i"es due south of /. -ind the "atitude of Q. A% ar;sB

Q terletak 1*00 batu nauti+al ke elatan J. 'ari latitud ba"i Q. $2 markah&


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#ap"e %

P(50oN,70oW), Q, R and 6 are four points on the surface of the earth. PQ is the diaeter

of the para""e" of "atitude of 50o

N and P6 is the diaeter of the earth. R "ies due south ofQ and the shortest distance fro Q to R easured a"on the surface of the earth is 5 00

nautica" i"es.

P(0o, -0o), Q, / dan ialah empat titik di permukaan bumi. PQ ialah diameter

elarian latitud 0o dan P ialah diameter bumi.. / terletak ke elatan Q dan !arak

terpendek dari Q ke / diukur di epan!an" permukaan bumi ialah 400 batu nautikal.

(a) #tate the "onitude of Q A% ar;sB

N#atakan lon"itud ba"i Q. $2 markah&

($) #tate the "atitude of 6. A% ar;sB N#atakan latitud ba"i . $2 markah&

(c) -ind the "atitude of R. A3 ar;sB

'ari latitud ba"i /. $% markah&

(d) a"cu"ate the distance, in nautica" i"e, fro P to Q easured a"on the coon

para""e" of "atitude. A3 ar;sB

itun" !arak, dalam batu nautikal, dari P ke Q di ukur epan!an" elarian latitud

epun#a $% markah&

(e) a"cu"ate the tie ta;en $> an aerop"ane to f"> fro P to Q easured a"on the

coon para""e" of "atitude and then it f"e! due south to R,if it trave""ed at an averae speed of '00 ;nots. A% ar;sB

itun" maa #an" diambil oleh ebuah kapal terban" untuk terban" dari P ke Q

diukur epan!an" elarian latitud epun#a dan kemudian terban" arah ke elatan ke /, !ika purata la!u eluruh per!alanan kapal terban" itu ialah 00 knot. $2 markah&


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2ns!ers (*arth as a sphere)

1(a) Q C (70o

#,15o

*), ($) R C (70o

N,15o

N)

%(a) + C (1'oN,13%oW), ($) C (1'o#,13%oW)

3(a) G C (0oN,0o*), ($) C ('5o#,0o*)

(a) & C (%0oN,o*), ($) + C (%0oN,5oW), (c) C (55o#,35o*)

5(a) %00 n.., ($) 7%00 n..

'. 00 n.. 13(a) 1%00 n.., ($) 3300 n..

7. ' '00 n.. 1. %5oN

. 51.5oN 15. 050 n..

. 35o# 1'. 5 hrs.

10. 3 0 n.. 17.(a) ' hrs, ($) '00cos0o AC 5.' n.B

11. o* 1. A3'00cos0oD %100B 500 hrs. AC.71 hrsB

1% (a) 3'00 n.., 1. 55

($) 5 00 n.. %0. %5o*.


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2ns!ers

#ap"e 1. (a) & C (0o

#,70o

W)

($)o0cos'0

%100, '.3o*

(c) (50D50)'0, ' 000 n..

(d)'0

1)00, 10oN

#ap"e %. (a) "onitude of Q C 110o*

($) "atitude of 6 C 50o#

(c)'0

5(00, 0o#

(d) 10('0)(cos50o) AC'5.% n.B

(e)'00

500)'0)(cos'0(10 + AC%0.5' hrsB

16 earth as a sphere

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