LATITUDES AND LONGITUDES

1.The positions of two towns A and B on the Earth’s surface are and  respectively.

1. a) Find the difference in longitude between towns A and B. (2MKS)
2. b) Given that the radius of Earth is 6370km, calculate the distance between towns A and B.

(3MKS)

1. c) Another town C is 840 km due east of town B and on the same latitude as towns A and B. Find the longitude of town C. (3MKS)
2. d) What is the time difference between towns A and B and towns A and C to the nearest minute?

(2MKS)

2.Two towns A and B lie on the same parallel of latitude 60⁰N if the longitudes of A and B are 42⁰W and 29⁰E respectively.

• Find the distance between A and B in nautical miles along the parallel of latitude.

(2mks)

• Find the local time at A if at B is 1.00pm. (2mks).
• Find the shortest distance between A and B along the earth’s surface in km. (2mks)(Take )
• If C is another town due south of A and 10010km away from A, find the coordinate C. (3mks)

3. A plane leaves an airport x (41.5⁰N, 36.4⁰W) at 9.00a.m. and flies due North to airport y on latitude 53.2⁰N.

• Calculate the distance covered by the plane in kilometers. (3mks)
• After stopping for 30 minutes to refuel at Y, the plane then flies due east to airport Z, 2500km from Y. Find:-
  • The position of Z.
  • The time the plane lands at Z, if its speed is 500km/h.

(Take the value of π as ²²/₇ and radius of the earth as 6370km)      (7mks)

 

 

 

 

 

4.The positions of two towns on the surface of the earth are given as A(30⁰S, 20⁰W) and B(30⁰S, 80⁰E)

Find

1. a) the difference in longitude             2mk

 

the distance between the two towns along a parallel of latitude in

(i)  km (take the radius of the earth as 6370km and p = ²²/₇)                                               3mks

 

(ii)  nm                                                                                                                                    2mks

 

1. c) Find the local time in town B when it is 1:45pm in town A. 3mks

 

5.A jet flies from town Q (60⁰S, 24⁰E) to town R (60⁰S,10⁰W) and then due north for 1200 nautical miles to town S

(a)          Obtain the latitude of S                                                                              (3mks

(b)          Calculate the distance between Q and R in

(i) Nautical miles                                                                                          (3mks)

(ii)           Km                                                                                                   (2mks)

(c)           Find the total flight time if the jet flies at an average speed of 800 knots            (2mks

 

6.A plane leaves an airport P(10⁰S,62⁰E) and flies due north at 800km/h.

(a)          Find its position after 2 hrs.                                                                                                     (3mks)

(b)          The plane turns and flies at the same speed due west. It reaches Q longitude of 12⁰W.

(i)            Find the distance it has travelled in nautical miles                               (3mks)

(ii)           Find the time it has taken (Take the radius of the earth to be 6370km and 1 nautical mile to be 1.853km)                                                                                   (2mks)

(c)           If the local time at P was 1300 hrs when it reached Q, Find the local time at Q when it

landed at Q .                                                                                                                (2mks)

7. Two points P and Q are found on the earth’s surface. The position of P is (52⁰S, 66⁰W)

and Q (52⁰S, 114⁰E). Using earth’s radius = 6370km:

• Find the difference in longitude between two points P and Q.          (1mk)

 

• Calculate the shortest distance between points P and Q along:-
  • The Latitude in km (to 1 whole number). (2mks)
  • The Longitude in km (to one whole number).     (3mks

 

• A plane travelling at 800km/hr leaves point P at 10.00am and sails through South Pole to point Q. Find the local time the plane arrives at point Q to the nearest minutes.     (4mks)

 

8.A jet flies from town Q (60⁰S, 24⁰E) to town R (60⁰S,10⁰W) and then due north for 1200 nautical miles to town S

(a)          Obtain the latitude of S                                                                                    (3mks)

(b)          Calculate the distance between Q and R in

(i) Nautical miles                                                                                                 (3mks)

(ii)           Km                                                                                                                     (2mks)

(c)           Find the total flight time if the jet flies at an average speed of 800 knots           (2mks)

 

 

 

 

 

 

 

 

 

 

3.

(a) 71 x 60 cos 60 n.m = 2130 n.m (b)71 x 4min = 284 min  4hrs 44 min 1300 – 4hrs 44min   = 8.16 am (c) (d)

M1   A1     M1 A1 M1   M1 A1 M1 M1 A1

üsubst       1300 – 4hrs 44 min

 

 

 

3.

 

 

 

 

 

 

 

 

 

 

 

 

SCHEME

1.Longitude = Distance = Longitude of town C A and B A and C

M1 A1       M1,A1

4.

(a)  x(41.50N, 56.40W) y(53.20N, 36.40W) Angle diff = (53.2 – 41.5)0 = 11.70 ℓ = (11.7 x 22 x 2 x 6370)km 360     7 =  1301.3km   (b)  (i)    y (53.20N, 56.40W) z (53.20N, ___x___)   = (  x   x 22 x 2 x 6370 cos 83.20) 360     7 =   2500km   x (11 x 91 cos 3.2)  = 2500 9   x =        2500 x 9 11 x 91 cos 53.40   x =      2500 x 9 11 x 91 x 0.5996   =   22500 599.599 = 37.520 37.52 – 36.40 = 1.120E Z(53.20N, 1.120E)   (ii) T = (1301.3)hrs 500 = 2.6026hrs = 2hrs 36mins 15mins x to z took 2hrs 36mins Past time – 30 mins   15min z – 4 – 2500km   Time taken (2500)hrs 500 = 5hrs Total time = 2.36 + 30 5.00 = 8.06   9.00 8.06 17.06 12.00 5.06pm	M1   M1     A1           M1             M1                   M1                       M1       M1             A1
	10

4.

S(S, LOW)         S(s,10w) Longitude difference a) Longitude difference (s-60)60 = 1200 great circle 60s – 3600 = 1200 60s = 4800 60         60 S = 800N b) longitudinal difference = 10+24 = 340 i) d = 60q cos x = 60 x 34 cos 600 = 1020nm ii) distance = 1nm = 1.853km \1020nm = ? (1020 x 1.853) = 1.890.06km c) Time between QR 1020 + 1200 800       800 111/40 + 1½ = 2 31/40 hrs

M1   M1   A1     M1   A1     M1   A1       M1 A1

5.6

 

(b) 74×60cos4.4⁰

=4426.9nm

 

(c)

= 10hrs15min

 

• P(10⁰S,62⁰E), Q(4.4⁰N,2⁰W)

 

 

8.

• 114⁰ + 66⁰ = 180⁰√B1

 

• (i) 180 x 2 x 3.142 x 6370 cos 520√B1

360

 

12322km or 12326km√B1 using Л= 22√A1

7

 

 

(ii) 76√B1 x 2 x 3.142 x 6370√M1

360

=  8451km or 8453km using Л= 22

7

• t = s = 8451√M1

v     800

 

=  10.56hrs√M1

=  10hrs 34min√A1

Time is 8.34pm√B1

 

8.

S(S, LOW)         S(s,10w) Longitude difference a) Longitude difference (s-60)60 = 1200 great circle 60s – 3600 = 1200 60s = 4800 60         60 S = 800N b) longitudinal difference = 10+24 = 340 i) d = 60q cos x = 60 x 34 cos 600 = 1020nm ii) distance = 1nm = 1.853km \1020nm = ? (1020 x 1.853) = 1.890.06km c) Time between QR 1020 + 1200 800       800 111/40 + 1½ = 2 31/40 hrs

M1   M1   A1     M1   A1     M1   A1       M1 A1