Question

find the magnitudes of the horizontal and vertical components for the vector v, if α is the direction angle of v from the horizontal. α = 249.4°, ||v|| = 787 the magnitude of the horizontal component of v is (round to the nearest integer as needed.)

Explanation:

Step1: Recall horizontal component formula

The horizontal component \( v_x = |\mathbf{v}| \cos(\alpha) \)

Step2: Substitute values

\( v_x = 787 \cos(249.4^\circ) \)

Step3: Calculate cosine value

\( \cos(249.4^\circ) = \cos(180^\circ + 69.4^\circ) = -\cos(69.4^\circ) \approx -0.3527 \)

Step4: Compute result

\( v_x \approx 787 \times (-0.3527) \approx -277.6 \)

Step5: Round to nearest integer

\( v_x \approx -278 \)

Answer:

-278