Question

if the magnitude of a vector is 23, and the angle it makes with the x - axis is 32°, what is its horizontal vector component? round all answers to the nearest hundredth.

Explanation:

Step1: Recall vector - component formula

The horizontal component of a vector $\vec{v}$ with magnitude $|\vec{v}|$ and angle $\theta$ with the $x$-axis is given by $v_x = |\vec{v}|\cos\theta$.

Step2: Substitute given values

We are given that $|\vec{v}| = 23$ and $\theta=32^{\circ}$. So, $v_x = 23\times\cos(32^{\circ})$.
Since $\cos(32^{\circ})\approx0.848$, then $v_x = 23\times0.848 = 19.504$.

Step3: Round the result

Rounding $19.504$ to the nearest hundredth, we get $v_x\approx19.50$.

Answer:

$19.50$