Vector v has the given magnitude and direction. Find the magnitude of the indicated component of v rounded to the nearest tenth when necessary.
-$\alpha = 25.8 ^ { \circ } , | \mathbf { v } | = 64.2$; Find the horizontal component of $\mathbf { v }$.
A) $85.7$
B) $57.8$
C) $29.9$
D) $27.9$

Question

Quizplus · Accepted Answer

The horizontal component of a vector can be found using the formula $v_{x} = |v| \cos(\alpha)$, where $|v|$ is the magnitude of the vector and $\alpha$ is the angle it makes with the horizontal. Plugging in the given values, $v_{x} = 64.2 \cos(25.8^\circ)$, which approximately equals 57.8.

Vector V Has the Given Magnitude and Direction α=25.8∘,∣v∣=64.2\alpha = 25.8 ^ { \circ } , | \mathbf { v } | = 64.2α=25.8∘,∣v∣=64.2

Vector V Has the Given Magnitude and Direction $\alpha = 25.8 ^ { \circ } , | \mathbf { v } | = 64.2$