142k views
3 votes
Instructions: Select the correct answer.

Vector u has a magnitude of 5 units and a direction angle of 30°. Vector v has a magnitude of 7 units and a direction angle of 120°. What is the direction angle of their vector sum?


A.) 82.21°


B.) 84.46°


C.) 85.11°


D.) 86.13°

User SMM
by
7.5k points

1 Answer

6 votes

Answer:

84.463°

Explanation:

Determine the x- and y-components of these two vectors. Sum up the x-comps and the y-comps separately, and then find the magnitude and direction of the vector sum:

x-comps:

5 cos 30° + 7 cos 120° = 5(0.866) + 7(-0.5) = 0.83

y-comps:

5 sin 30° + 7 sin 120° = 5(0.5) + 7(0.866) = 2.5 + 6.062 = 8.562

Both components are in Quadrant I, so the direction angle ∅ is between 0° and 90°: ∅ = arcctan 8.562/0.83 = arctan 10.316 = 1.474 radian, or

1.474 rad 180°

-------------- * ----------- = 84.463°

1 π

User Snowmantw
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories