A man walks the distance of 8km in a direction of 20degrees east the walks another 6km in a direction 50degrees south east. Using vector diagrams find the magnitude and direction of the final displacement relative to the starting point.
What grade is this?
we can't do a vector diagram here.
draw an arrow E, of length to represent 8 units. Then from the tip of the arrow, draw a vector 50 deg south of East of length 6. Now, measure the length from the original origin to the final tip. Convert that length to km.
To find the magnitude and direction of the final displacement relative to the starting point, we can use vector addition by creating a vector diagram. Here are the steps to do so:
Step 1: Draw a coordinate system. Choose a convenient scale, such that we can represent distances accurately on the diagram.
Step 2: Start by drawing a vector representing the first leg of the journey, 8km in a direction of 20 degrees east. To do this, draw a line segment of 8 units in length, making an angle of 20 degrees to the east from the starting point.
Step 3: Next, draw a vector representing the second leg of the journey, 6km in a direction of 50 degrees south east. To do this, draw a line segment of 6 units in length, making an angle of 50 degrees to the south east from the tip of the first vector.
Step 4: Now, draw a line from the starting point to the tip of the second vector. This line represents the final displacement relative to the starting point.
Step 5: Measure the length of this line segment. This magnitude represents the distance of the final displacement relative to the starting point.
Step 6: Measure the angle that this line segment makes with the positive x-axis (east direction). This angle represents the direction of the final displacement relative to the starting point.
Step 7: Convert the magnitude and direction of the final displacement to the appropriate units if necessary.
By following these steps, you will be able to determine the magnitude and direction of the final displacement relative to the starting point.