Question

"Convert the resultant vector into its x and y components.

225 N at 12 degrees

a. (220.1 N, 46.8 N)
b. (201.1 N, 10.8 N)
c. (222.3 N, 37.4 N)
d. (45.8 N, 201.1 N)"

Answer 1

The resultant vector with a magnitude of 225 N at 12 degrees can be broken down into x and y components using trigonometry, resulting in the x-component being 220.1 N and the y-component being 46.8 N, which matches answer choice (a).

Step-by-step explanation:

To convert a resultant vector into its x and y components, we use trigonometric relations. Given a resultant vector of 225 N at 12 degrees above the x-axis, we can determine the components as follows:

• The x-component (Fx) is given by: Fx = magnitude * cos(θ) = 225 N * cos(12°)
• The y-component (Fy) is given by: Fy = magnitude * sin(θ) = 225 N * sin(12°)

Performing the calculations:

• Fx ≈ 220.1 N
• Fy ≈ 46.8 N

Therefore, the vector components in x and y directions are (220.1 N, 46.8 N), which corresponds to answer choice (a).