Vector v has the given magnitude and direction. Find the magnitude of the indicated component of v rounded to the nearest tenth when necessary.
-$\alpha = 35.7 ^ { \circ } , | \mathbf { v } | = 368$; Find the vertical component of $\mathbf { v }$.
A) $298.8$
B) $214.7$
C) $513.5$
D) $84.1$

Question

Quizplus · Accepted Answer

The vertical component of a vector can be found using the sine of the angle and the magnitude of the vector. For vector $\mathbf{v}$ with magnitude $|\mathbf{v}| = 368$ and direction $\alpha = 35.7^\circ$, the vertical component $v_y$ is given by $v_y = |\mathbf{v}| \sin(\alpha)$. Calculating this gives $v_y = 368 \sin(35.7^\circ) \approx 214.7$.

Vector V Has the Given Magnitude and Direction α=35.7∘,∣v∣=368\alpha = 35.7 ^ { \circ } , | \mathbf { v } | = 368α=35.7∘,∣v∣=368

Vector V Has the Given Magnitude and Direction $\alpha = 35.7 ^ { \circ } , | \mathbf { v } | = 368$