Question

Vector A has a magnitude if 7.0 m and points 30 degrees east of north. Vector B has a magnitude of 5.0 m and points 30 degrees west of south. The resultant vector A+B is given by.... (HINT: solve by lining up the vectors head to tail!!!!!!!!)

Answer 1

To obtain the resultant vector A+B, we break down vectors A and B into their east/west and north/south components, combine them respectively, and use the Pythagorean theorem to find the magnitude of the resultant vector. The angle θ of the resultant vector from the eastward axis can be obtained by taking the arctan of the ratio of the northward and eastward components.

Step-by-step explanation:

To find the resultant vector A+B, we use vector addition by aligning the vectors head to tail. For vector A with a magnitude of 7.0 m pointing 30 degrees east of north, we can break it down into its components. The northward component of vector A is Ay = 7 cos(30°) and the eastward component is Ax = 7 sin(30°).

Similarly, for vector B with a magnitude of 5.0 m pointing 30 degrees west of south, its components would be southward By = 5 cos(30°) and westward Bx = -5 sin(30°) (negative because it points westward).

Adding the components, we get the total eastward component: Ax + Bx and the total northward component: Ay - By (subtracting By because it points southward). The magnitude of the resultant vector R can be found using the Pythagorean theorem:

R = √((Ax + Bx)^2 + (Ay - By)^2)

And the direction of R with respect to the east, θ, can be found using the formula tan(θ) = (Ay - By) / (Ax + Bx), where you then take the arctan to find the angle θ.