Question

A vector representing 140 N is oriented at 28◦ with the horizontal.

What is the magnitude of its horizontal component?
Answer in units of N.
What is the magnitude of its vertical component?
Answer in units of N.

Answer 1

The horizontal component of a 140 N force vector at 28° to the horizontal is approximately 123.61 N, and the vertical component is approximately 65.73 N. Trigonometric functions such as cosine and sine are used to calculate these values.

Step-by-step explanation:

To find the horizontal and vertical components of a force vector, you use trigonometry. For a vector with a magnitude of 140 N oriented at 28° with the horizontal, the horizontal component (Fx) is found using the cosine function:

Fx = F · cos(θ) = 140 N · cos(28°)

The vertical component (Fy) is found using the sine function:

Fy = F · sin(θ) = 140 N · sin(28°)

Plugging in the values:

• Fx ≈ 140 N · 0.88295 = 123.61 N
• Fy ≈ 140 N · 0.46947 = 65.73 N

The magnitudes of the horizontal and vertical components are approximately 123.61 N and 65.73 N, respectively.