Features and Location of Places
The Equator, Great Circle, Small Circles, Meridian, Latitudes and Longitudes
Describe the equator, great circle, small circles, meridian, latitudes and longitudes
Definition of latitude and longitude
Distance along Small Circles
Calculate distance along small circles
Suppose
P and Q are places west or east of each other, i.e they lie on the same
circle of latitude. Then when you travel due east or west from P to Q
you travel along an arc of the circle of latitude.
P and Q are places west or east of each other, i.e they lie on the same
circle of latitude. Then when you travel due east or west from P to Q
you travel along an arc of the circle of latitude.
The
situation here is slightly different from that of the previous section.
While circles of longitude all have the same length, circles of
latitude get smaller as they get nearer the poles.
situation here is slightly different from that of the previous section.
While circles of longitude all have the same length, circles of
latitude get smaller as they get nearer the poles.
Consider the circle of latitude 50°S. Let its radius be r km.


Nautical miles

Example 8
Find the distance in km and nm along a circle of latitude between (20°N, 30°E) and (20°N, 40°W).
Solution:
Both places are on latitude 20°N. The difference in longitude is 70°. Use the formula for distance.
Distance = 111.7 cos20° x 70°. Hence the distance in nautical miles is 60 x 70 x cos20°
The distance isĀ 3,950 nm.
Example 9
A ship starts at (40°S, 30°W) and sails due west for 1,000 km. Find its new latitude and longitude.

Example 10
A ship sails west from (20°S, 15°E) to (20°S, 23°E), taking 37 hours. Find speed, in knots and in kms per hr.

Exercise 4
Consider the following Questions.

Navigation
Suppose
a ship is sailing in a sea current, or that a plane is flying in a
wind. Then the course set the ship or plane is not the direction that it
will move in. the actual direction and speed can be found either by
scale or by the use of Pythagorasās theorem and trigonometry.
a ship is sailing in a sea current, or that a plane is flying in a
wind. Then the course set the ship or plane is not the direction that it
will move in. the actual direction and speed can be found either by
scale or by the use of Pythagorasās theorem and trigonometry.
Draw
the line representing the motion of the ship relative to the water. At
the end of this line draw a line representing the current. Draw the
third side of the triangle. This side, shown with a double ā headed
arrow, is the actual course of ship.
the line representing the motion of the ship relative to the water. At
the end of this line draw a line representing the current. Draw the
third side of the triangle. This side, shown with a double ā headed
arrow, is the actual course of ship.
Example 11
A
ship sets course due east. In still water the ship can sail at 15km/hr.
There is a current following due south of 4kkm/hr. use a scale drawing
to find.
ship sets course due east. In still water the ship can sail at 15km/hr.
There is a current following due south of 4kkm/hr. use a scale drawing
to find.
- The speed of the ship
- The bearing of the sip.
Solution:
In
one hour the ship sails 15km east relative to the water. Draw a
horizontal line of length 15cm. In one hour the current pulls the ship
4km south. At the end of the horizontal line, draw a vertical line of
length 4cm.
one hour the ship sails 15km east relative to the water. Draw a
horizontal line of length 15cm. In one hour the current pulls the ship
4km south. At the end of the horizontal line, draw a vertical line of
length 4cm.

Example 12
The ship of example 10 needs to travel due east. Calculate the following.
- What course should be set?
- How long will the ship take to cover 120km?
Solution
The ship needs to set a course slightly north of east, consider the following diagram.

Note:
With no current, the journey would take 8hrs. The journey takes
slightly longer when there is a current.Suppose a ship or a plane does
not directly reach a position. We can still find how close the ship or
plane is to the position.
With no current, the journey would take 8hrs. The journey takes
slightly longer when there is a current.Suppose a ship or a plane does
not directly reach a position. We can still find how close the ship or
plane is to the position.

Example 13
A
small island is 200km away on a bearing of 075°. A ship sails on a
bearing of 070°.Find the closest that the ship is to the island.
small island is 200km away on a bearing of 075°. A ship sails on a
bearing of 070°.Find the closest that the ship is to the island.

Exercise 5
1. Find the difference in longitude between Cape Town (34°S, 18°E) and Buenos Aires (34°S, 58°W)
2. A ship startsat (15°N, 30°W) and sails south for 2,500km. Where does it end up?
3. Find thedistance in km along circle of latitude between cape Town and Buenos aires (see question 2)
4. A plane starts at (37°S, 23°W) and flies east for 1,500 km. where does it end up?
5. Find thedistance in nau
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