a car travels straight for 20 miles on a road that is 30° north of east. what is the east component of the…
a car travels straight for 20 miles on a road that is 30° north of east. what is the east component of the cars displacement to the nearest tenth of a mile?\n-17.3 miles\n-10.0 miles\n10.0 miles\n17.3 miles
Answer
Explanation:
Step1: Recall component - formula
The formula for the x - component (east - west direction) of a vector with magnitude $R$ and direction $\theta$ is $R_x = R\cos\theta$. Here, $R = 20$ miles and $\theta=30^{\circ}$.
Step2: Calculate the east - component
$R_x=20\times\cos(30^{\circ})$. Since $\cos(30^{\circ})=\frac{\sqrt{3}}{2}\approx0.866$, then $R_x = 20\times0.866 = 17.32\approx17.3$ miles.
Answer:
D. 17.3 miles