Solve the problem.
-An airplane is flying on a bearing of $310 ^ { \circ }$ at $560 \mathrm { mph }$. Find the component form of the velocity of the airplane. Round your answer to the nearest hundredth.
A) $\approx \langle ( 359.72 , - 429.18 )$
B) $\approx \langle - 294.19,476.50 \rangle$
C) $ \approx\langle-14.28,-18.87\rangle $
D) $\approx \langle - 517.22 , - 214.66 \rangle$

Question

Solve the problem.
-An airplane is flying on a bearing of $310 ^ { \circ }$ at $560 \mathrm { mph }$. Find the component form of the velocity of the airplane. Round your answer to the nearest hundredth.
A) $\approx \langle ( 359.72 , - 429.18 )$
B) $\approx \langle - 294.19,476.50 \rangle$
C) $  \approx\langle-14.28,-18.87\rangle $
D) $\approx \langle - 517.22 , - 214.66 \rangle$

Quizplus · Accepted Answer

The component form of the velocity can be found using the formulas: $v_x = v \cdot \cos(\theta)$ and $v_y = v \cdot \sin(\theta)$, where $v$ is the speed and $\theta$ is the angle. For a bearing of $310^\circ$, the angle from the positive x-axis is $360^\circ - 310^\circ = 50^\circ$. Thus, $v_x = 560 \cdot \cos(50^\circ)$ and $v_y = 560 \cdot \sin(50^\circ)$, which gives approximately $\langle -294.19, 476.50 \rangle$.

Solve the Problem 310∘310 ^ { \circ }310∘ At 560mph560 \mathrm { mph }560mph

Solve the Problem $310 ^ { \circ }$ At $560 \mathrm { mph }$