To find the magnitude and direction of the resultant vector, we need to add the given vectors A and B.
Given:
Vector A magnitude (|A|) = 20 m
Vector B magnitude (|B|) = 10 m
To add vectors A and B, we can use the vector addition formula:
Resultant vector R = A + B
To calculate the magnitude of the resultant vector, we can use the Pythagorean theorem:
|R| = sqrt((Ax + Bx)^2 + (Ay + By)^2)
where Ax and Ay are the x and y components of vector A, and Bx and By are the x and y components of vector B.
Since we don't have information about the direction of the vectors, we'll assume that vector A is aligned with the positive x-axis and vector B is aligned with the positive y-axis.
Using this assumption, we can break down the vectors into their x and y components:
Vector A:
Ax = |A| = 20 m (since it is aligned with the positive x-axis)
Ay = 0 (since it is aligned with the positive x-axis)
Vector B:
Bx = 0 (since it is aligned with the positive y-axis)
By = |B| = 10 m (since it is aligned with the positive y-axis)
Now we can calculate the magnitude of the resultant vector:
|R| = sqrt((Ax + Bx)^2 + (Ay + By)^2)
= sqrt((20)^2 + (0 + 10)^2)
= sqrt(400 + 100)
= sqrt(500)
≈ 22.36 m
So, the magnitude of the resultant vector is approximately 22.36 m.
To find the direction of the resultant vector, we can use trigonometry. The angle θ can be calculated as:
θ = atan2((Ay + By), (Ax + Bx))
θ = atan2(10, 20)
≈ 26.57 degrees
Therefore, the direction of the resultant vector is approximately 26.57 degrees relative to the positive x-axis.
In summary:
Magnitude of the resultant vector: approximately 22.36 m
Direction of the resultant vector: approximately 26.57 degrees