Question
A car travels straight for 20 miles on a road that is 30° north of east. What is the east component of the car’s displacement to the nearest tenth of a mile?
-17.3 miles
-10.0 miles
10.0 miles
17.3 miles
-17.3 miles
-10.0 miles
10.0 miles
17.3 miles
Answers
GPT-4o mini
To find the east component of the car’s displacement, we can use trigonometry. Given that the car travels 20 miles at an angle of 30° north of east, we can calculate the eastward displacement using the cosine function, because the east component corresponds to the adjacent side of the right triangle formed.
The formula for the east component (E) is:
\[
E = \text{total distance} \times \cos(\theta)
\]
Where:
- total distance = 20 miles
- \(\theta\) = 30°
Calculating the east component:
\[
E = 20 \times \cos(30°)
\]
We know that \(\cos(30°) = \frac{\sqrt{3}}{2} \approx 0.866\). Now we substitute this value into the equation:
\[
E = 20 \times 0.866 \approx 17.32
\]
Rounding to the nearest tenth of a mile, the east component of the car’s displacement is approximately:
**17.3 miles**
So the answer is **17.3 miles**.
The formula for the east component (E) is:
\[
E = \text{total distance} \times \cos(\theta)
\]
Where:
- total distance = 20 miles
- \(\theta\) = 30°
Calculating the east component:
\[
E = 20 \times \cos(30°)
\]
We know that \(\cos(30°) = \frac{\sqrt{3}}{2} \approx 0.866\). Now we substitute this value into the equation:
\[
E = 20 \times 0.866 \approx 17.32
\]
Rounding to the nearest tenth of a mile, the east component of the car’s displacement is approximately:
**17.3 miles**
So the answer is **17.3 miles**.