Ask Question
28 February, 03:41

Displacement vectors A, B, and C add up to a total of zero. Vector A has a magnitude of 1550 m and a direction of 25.6° north of east. Vector B has a direction of 41.0° east of south, and vector C has a direction of 35.1° north of west. Find the magnitudes of vector B and vector C.

+4
Answers (1)
  1. 28 February, 04:11
    0
    B = 5626.77 m

    C = 6220. 5 m

    Explanation:

    Because the sum of the vectors must be equal to zero, then the result force in x and the result force in y must be zero.

    We propose 2 equations x-y to solve the problem:

    Rx : resulting from forces at x

    Ry: resulting from forces at y

    Rx = Ax+Bx+Cx=0

    Ry = Ay+By+Cy=0

    Ax = 1550 * cos25.6° = 1397.84

    Ay = 1550 * sin25.6° = 669.73

    Bx = B*sin41° = 0.656B

    By = - B*cos41° = - 0.7547 B

    Cx = - C*cos35.1° = - 0.8181 C

    Cy = C * sin35.1° = 0.575 C

    Rx = 1397.84+0.656B-0.8181 C=0

    Ry = 669.73-0.7547 B + 0.575 C=0

    System of 2 equations with 2 incognites:

    +0.656B-0.8181 C = - 1397.84

    -0.7547 B + 0.575 C = - 669.73

    Resolving the system:

    B = 5626.77 m

    C = 6220. 5 m
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Displacement vectors A, B, and C add up to a total of zero. Vector A has a magnitude of 1550 m and a direction of 25.6° north of east. ...” in 📙 Physics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers