Question
A force of 89 N is exerted 28° north of east. What is the eastward component of this force?
Answers
GPT-4o mini
To find the eastward component of the force, you can use the cosine of the angle. The formula for the eastward component \(F_{\text{east}}\) is given by:
\[
F_{\text{east}} = F \cdot \cos(\theta)
\]
where:
- \(F\) is the total force (89 N),
- \(\theta\) is the angle (28°).
Now, calculate the eastward component:
\[
F_{\text{east}} = 89 \, \text{N} \cdot \cos(28^\circ)
\]
Using a calculator to find \(\cos(28^\circ)\):
\[
\cos(28^\circ) \approx 0.8829
\]
Now multiply:
\[
F_{\text{east}} \approx 89 \cdot 0.8829 \approx 78.49 \, \text{N}
\]
Thus, the eastward component of the force is approximately **78.49 N**.
\[
F_{\text{east}} = F \cdot \cos(\theta)
\]
where:
- \(F\) is the total force (89 N),
- \(\theta\) is the angle (28°).
Now, calculate the eastward component:
\[
F_{\text{east}} = 89 \, \text{N} \cdot \cos(28^\circ)
\]
Using a calculator to find \(\cos(28^\circ)\):
\[
\cos(28^\circ) \approx 0.8829
\]
Now multiply:
\[
F_{\text{east}} \approx 89 \cdot 0.8829 \approx 78.49 \, \text{N}
\]
Thus, the eastward component of the force is approximately **78.49 N**.