Question

find the magnitudes of the horizontal and vertical components of v, if α is the direction angle of v from the horizontal. α = 65°10, |v| = 11.6 the horizontal component of v is 4.9 (round to the nearest tenth as needed.) the vertical component of v is (round to the nearest tenth as needed.)

Explanation:

Step1: Calculate horizontal component

$v_x = |v| \cos(\alpha) = 11.6 \cos(65^\circ)$
$\cos(65^\circ) \approx 0.4226$, so $v_x \approx 11.6 \times 0.4226 \approx 4.9$

Step2: Calculate vertical component

$v_y = |v| \sin(\alpha) = 11.6 \sin(65^\circ)$
$\sin(65^\circ) \approx 0.9063$, so $v_y \approx 11.6 \times 0.9063 \approx 10.5$

Answer:

Horizontal component: 4.9
Vertical component: 10.5