A plane flies from base camp to lake A, a distance of 300 km at a direction of 20.0° north of east. After dropping off supplies, the plane flies to lake B, which is 210 km and 30.0° west of north from lake A. Graphically determine the distance and direction from lake B to the base camp.
GRAPHICALLY? Draw the lines, HEAD to tail with your protractor and scale. Where is the last head?
To graphically determine the distance and direction from lake B to the base camp, we can break down the given information into vectors and use vector addition.
Step 1: Draw a diagram
Start by drawing a reference frame or coordinate system. We can choose a horizontal axis (east) and vertical axis (north). Place the base camp at the origin (0,0) and label it accordingly. Then, draw a line representing the plane's flight path from the base camp to lake A at a direction of 20.0° north of east. Label it as vector A.
Step 2: Represent vector A
Since vector A is given as a distance of 300 km at a direction of 20.0° north of east, we can represent it as a directed line segment. Measure 300 km from the base camp in the direction 20.0° north of east and draw a line segment representing vector A.
Step 3: Determine vector B
To determine vector B, we need to consider the plane's flight from lake A to lake B. It is given that lake B is 210 km and 30.0° west of north from lake A. This means that the direction from lake A to lake B is 30.0° counter-clockwise from the north direction. Therefore, from the endpoint of vector A (lake A), measure a distance of 210 km in the direction 30.0° west of north and draw a line segment representing vector B.
Step 4: Analyze the diagram
You should now have a diagram with vector A representing the flight from the base camp to lake A, and vector B representing the flight from lake A to lake B. To find the distance and direction from lake B to the base camp, we need to find the resultant vector when vectors A and B are added together.
Step 5: Add vectors A and B
Using graphical vector addition, draw a vector starting from the tail of vector B and ending at the head of vector A. This resultant vector represents the displacement (distance and direction) from lake B to the base camp.
Step 6: Measure the resultant vector
Measure the magnitude (distance) of the resultant vector using a ruler or a scale. This will give you the distance from lake B to the base camp.
Step 7: Measure the direction of the resultant vector
Measure the angle (direction) that the resultant vector makes with the reference axis (north) using a protractor or angle measuring tool. This will give you the direction from lake B to the base camp.
By following these steps and analyzing the diagram, you can graphically determine the distance and direction from lake B to the base camp.