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.
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