Question

Vector A (A^→) points in the positive y-direction with a magnitude of 7.0 cm. If it is added to vector B (B^→), and the resultant vector C (C^→) has a magnitude of 18 cm at an angle of 120º, what are the components of vector B?

a) B_x = -9.0 cm, B_y = 12.0 cm
b) B_x = 12.0 cm, B_y = 9.0 cm
c) B_x = 9.0 cm, B_y = 12.0 cm
d) B_x = -12.0 cm, B_y = -9.0 cm

Answer 1

The resultant vector will be Bₓ = 12.0 cm,
`B_y` = 9.0 cm. Thus the correct option is b.

Step-by-step explanation:

To find the components of vector B, we need to start by breaking down the resultant vector C into its x and y components. Given that the magnitude of vector C is 18 cm and it makes an angle of 120º with the positive x-axis, we can use trigonometry to determine its x and y components.

The magnitude of the x-component (Cₓ) can be found using cosine:

Cₓ = C * cosθ

where θ is the angle between the vector and the x-axis.

Therefore, Cₓ = 18*cos(120º).

Similarly, the magnitude of the y-component
`(C_y)` can be found using sine:

`\(C_y = C * \sin(\theta)\)`

giving

`\(C_y = 18 * \sin(120)\)`.

Once we have the components of vector C, we subtract the known component of vector A (which points in the positive y-direction with a magnitude of 7.0 cm) from the resultant vector C. Vector A only has a y-component, so we subtract 7.0 cm from the y-component of vector C to find the y-component of vector B.

Therefore, the components of vector B are found by subtracting the known y-component of vector A from the y-component of vector C, resulting in Bₓ = 12.0 cm and
`B_y` = 9.0 cm.

Therefore, the correct option is b.