A port has two radar stations at P and Q which are 20 km apart.The radar at P is set to a range of 20 km,whilst the radar at Q is set to a range of 15 km.
a)draw a scale diagram to show the above information
b)Shade the region in which a ship must be sailing if it is only picked up by radar P.Label this region "a".
c)Shade the region in which a ship must be sailing if it is only picked up by radar Q.Label this region "b".
d)Identify the region in which a ship must be sailing if it is picked up by both radars.Label this region "c".
Note-a new scale diagram must be drawn for each sub question.The same diagram may not be used for all sub-questions.
scale
a) To draw a scale diagram, we need to establish a scale. Let's select a scale of 1 cm = 5 km.
b) To shade the region in which a ship must be sailing if it is only picked up by radar P, we draw a circle centered at P with a radius of 20 km.
c) To shade the region in which a ship must be sailing if it is only picked up by radar Q, we draw a circle centered at Q with a radius of 15 km.
d) To identify the region in which a ship must be sailing if it is picked up by both radars, we need to find the intersection of the two circles. This region will be the overlapping portion of both circles.
Here is a step-by-step breakdown of the process:
1) Draw a straight line segment to represent the 20 km distance between radar stations P and Q.
2) Select a point on the line segment and label it as P.
3) From point P, draw a circle with a radius of 20 km using a compass.
4) Select a point on the line segment that is 15 km away from point P, and label it as Q.
5) From point Q, draw a circle with a radius of 15 km using a compass.
6) Shade the region enclosed by the circle centered at P. Label this region as "a".
7) Shade the region enclosed by the circle centered at Q. Label this region as "b".
8) Identify the overlapping region of the two circles, and label it as "c".
Please note that I cannot physically draw the diagram for you, but I hope this step-by-step breakdown helps you create an accurate scale diagram.
a) To draw a scale diagram, we first need to determine the scale of the diagram. Let's choose a scale of 1 centimeter on the diagram to represent 5 kilometers in real life.
Place point P on the diagram and label it. From point P, draw a line segment 4 centimeters long (representing 20 km) in any direction. This line segment represents the range of radar P.
Next, place point Q on the diagram and label it. From point Q, draw a line segment 3 centimeters long (representing 15 km) in any direction. This line segment represents the range of radar Q.
Finally, draw a line to connect points P and Q. This line represents the distance between the two radar stations (20 km).
b) Shade the region where a ship can be detected by radar P only, within a range of 20 km from point P. Label this region as "a".
c) Shade the region where a ship can be detected by radar Q only, within a range of 15 km from point Q. Label this region as "b".
d) The region where a ship must be sailing to be detected by both radars is the intersection of regions "a" and "b". Shade this region and label it as "c".
Remember to adjust the scale and sizes of the regions appropriately while drawing the diagram.