Question

Question 16 of 16 > Vector C has a magnitude of 22.2 m and points in the -y-direction. Vectors A and B both have positive y-components, and make angles of a = 42.4° and B = 27.2° with the positive and negative x-axis, respectively. If the vector sum A + B + C = 0, what are the magnitudes of A and B? JA =

Answer 1

here,

vector A = A * ( cos(alpha) i + sin(alpha) j)

vector A = A * ( cos(42.4) i + sin(42.4) j) = A * ( 0.728 i + 0.674 j)

vector B = B * ( - cos(beta) i + sin(beta) j)

vector B = B * (- cos(27.2) i + sin(27.2) j) = B * ( 0.889 i + 0.457 j)

vector C = - 22 j

as A + B + C = 0

A * ( 0.728 i + 0.674 j) + B * (- cos(27.2) i + sin(27.2) j) - 22 j = 0

on copairing the components

A * ( 0.728 ) + B * (- cos(27.2) ) = 0 ....(1)

and

A * 0.674 + 0.457 * B = 22 ...(2)

from (1) and (2)

|A| = 20.99 units

|B| = 17.2 units