You are given three displacement vectors: with magnitude 5.0 m in the direction of 60o below the negative x-axis, vector, has an x-component of +2.5 m and a y-component of +6.0 m and vector has magnitude of 2.5 m in the negative y-axis.
three vectors: Break up each into component vectors, and add.
R= A + B + C
R= 5cos150 j +5sin150 i + 2.5 i + 6 j +2.5(-j)
check those, angles from + y axis.
To find the resultant displacement vector, we need to add all three displacement vectors together.
First, let's analyze the given information for each vector:
1. Vector A: Magnitude 5.0 m, direction 60 degrees below the negative x-axis.
To represent this vector in terms of its components, we need to use trigonometry.
The x-component of vector A can be found by using cosine function:
Ax = magnitude * cos(theta) = 5.0 m * cos(60 degrees)
Ax = 5.0 m * 0.5 = 2.5 m (positive direction)
The y-component of vector A can be found using sine function:
Ay = magnitude * sin(theta) = 5.0 m * sin(60 degrees)
Ay = 5.0 m * 0.866 = 4.33 m (positive direction)
So, vector A has an x-component of +2.5 m and a y-component of +4.33 m.
2. Vector B: X-component +2.5 m, y-component +6.0 m.
We already have the x and y components for this vector.
3. Vector C: Magnitude 2.5 m, along the negative y-axis.
Since this vector is along the negative y-axis, its x-component is zero (x = 0 m)
and the y-component is just the magnitude with the opposite sign.
So, vector C has an x-component of 0 m and a y-component of -2.5 m.
Now, let's find the resultant displacement vector by adding all the components together.
Resultant x-component (Rx): Ax + Bx + Cx = 2.5 m + 2.5 m + 0 m = 5.0 m
Resultant y-component (Ry): Ay + By + Cy = 4.33 m + 6.0 m - 2.5 m = 7.83 m
Therefore, the resultant displacement vector has an x-component of +5.0 m and a y-component of +7.83 m.