Displacement vector A is 4.5 km north. Displacement vector B is 3.0 km 50o N of E. Finds their resultant vector using the parallelogram method.
The diagonal z of the parallelogram is
z^2 = 4.5^2 + 3.0^2 - 2*4.5*3.0 cos140°
z = 7.07
4.5cis90° + 3.0 cis50° = 7.07 @ 74.17°
Can this be solved using the analytical method? If yes, can you show how to solved it? I’m having a hard time with my homework.
To find the resultant vector using the parallelogram method, follow these steps:
Step 1: Draw a scaled diagram of the two displacement vectors.
- Start by drawing a line representing vector A, 4.5 km long, pointing north.
- Then draw a line representing vector B, 3.0 km long, positioned 50 degrees north of east.
Step 2: Complete the parallelogram.
- Complete the parallelogram by drawing a line connecting the tail of vector A to the head of vector B.
Step 3: Measure the length and direction of the resultant vector.
- Measure the length of the line connecting the tails of vector A and B. This represents the magnitude of the resultant vector.
- Measure the angle between the line connecting the tails and the line representing vector A. This represents the direction of the resultant vector.
Step 4: Determine the values.
- Measure the length of the line in the diagram in step 3. Let's say it measures 6.2 cm.
- Measure the angle between the line connecting the tails and the line representing vector A. Let's say it measures 70 degrees.
Step 5: Convert the measurements back to vector form.
- Convert the length from centimeters to kilometers. If 1 cm represents 1 km, then the length of the resultant vector is 6.2 km.
- Convert the angle measured in degrees to a direction in relation to north. In this case, the resultant vector is 70 degrees north of east.
Therefore, the resultant vector using the parallelogram method is 6.2 km, 70 degrees north of east.
To find the resultant vector using the parallelogram method, we need to draw a parallelogram with the two given displacement vectors as adjacent sides. Here's how to do it step by step:
Step 1: Draw a horizontal line and label one end as the starting point. This will represent the initial position.
Step 2: From the starting point, draw a line in the direction of vector A (4.5 km north). Label the end of this line as point A.
Step 3: From point A, draw a line in the direction of vector B (3.0 km 50o N of E). The angle indicates that the line should be drawn 50o to the northeast of point A. Label the end of this line as point B.
Step 4: Connect the starting point to point B with a straight line. This represents vector B.
Step 5: Connect the starting point to point A with a straight line. This represents vector A.
Step 6: Complete the parallelogram by drawing lines parallel to vectors A and B from the endpoints of the opposite vector.
Step 7: The diagonal that connects the two opposite vectors represents the resultant vector. Label the end of this diagonal as point R.
Step 8: Measure the length and direction of the diagonal to determine the magnitude and direction of the resultant vector.
To measure the resultant vector, you can use a ruler to measure the length of the diagonal, and use a protractor to measure the angle that the diagonal makes with the horizontal line.
Note: The parallelogram method assumes that the vectors obey the parallelogram law of vector addition.