Vector A= a displacment of 20 m due east
Vector B= a displasment of 30 m due north
To find the resultant displacement when you add vector A (20 m due east) and vector B (30 m due north), you can use the Pythagorean theorem. Here's how you can do it:
1. Take a sheet of paper and draw a coordinate system. Label the x-axis as east/west (+x in the east direction) and the y-axis as north/south (+y in the north direction).
2. Locate the starting point (origin) of vector A (in this case, 0,0) on the coordinate system and draw an arrow for vector A in the east direction with a length of 20 units.
3. Locate the starting point of vector B (also at the origin) and draw an arrow for vector B in the north direction with a length of 30 units.
4. To find the resultant displacement, draw an arrow from the starting point of vector A to the endpoint of vector B. This arrow represents the sum of the displacements.
5. Now, we have created a right-angled triangle with vector A and vector B as its sides. The magnitude of the resultant displacement (R) can be calculated using the Pythagorean theorem: R^2 = A^2 + B^2.
6. Substitute the values for A and B: R^2 = (20)^2 + (30)^2.
7. Simplify the equation: R^2 = 400 + 900.
8. Add the values: R^2 = 1300.
9. Take the square root of both sides to find the magnitude of the resultant displacement: R ≈ √1300 ≈ 36.06 m.
10. To find the direction of the resultant displacement, you can use trigonometric functions. The angle between the resultant displacement and the positive x-axis can be found using the inverse tangent function: θ = tan^(-1)(B/A) = tan^(-1)(30/20) ≈ 56.31 degrees north of east.
Therefore, the resultant displacement when vector A and vector B are added is approximately 36.06 m in magnitude and is directed approximately 56.31 degrees north of east.