Question

A force of 89 N is exerted 28° north of east. What is the northward component of this force?

Group of answer choices

Answer 1

To find the northward component of a force that is exerted at an angle, you can use trigonometric functions. In this case, you want to find the northward (vertical) component of the force.

Given:
- Magnitude of the force (F) = 89 N
- Angle (θ) = 28° north of east

The northward component (F_north) can be calculated using the sine function:

\[
F_{\text{north}} = F \cdot \sin(\theta)
\]

Substituting the given values:

\[
F_{\text{north}} = 89 \, \text{N} \cdot \sin(28^\circ)
\]

Now, calculating the sine of 28 degrees:

\[
\sin(28^\circ) \approx 0.4695
\]

Now, substitute that value back into the equation:

\[
F_{\text{north}} \approx 89 \, \text{N} \cdot 0.4695 \approx 41.8 \, \text{N}
\]

Therefore, the northward component of the force is approximately **41.8 N**.