Question

Vector C has a magnitude 27.0 m and is in the direction of the negative y axis. Vectors A and B are at angles α = 44.4° and β = 28.2° up from the x axis respectively. If the vector sum A B C = 0, what are the magnitudes of A and B?

Vector C has a magnitude 27.0 m and is in the direction of the negative y axis. Vectors A and B are at angles alpha = 44.4degrees and beta = 28.2degrees up from the x axis respectively. If the vector sum A + B + C = 0, what are the magnitudes of A and B? |A| = Number 25.754 m |B| = Number 25.753 m There is a hint available! View the hint by clicking on the bottom divider bar, Click on the divider bar again to hide the hint. Close

Answer 1

The vector A is given as, 4 cos(44.4)i +Asin(44.4").j The vector B is given as, B-Bcos β(-)+ B si, pj --B cos (28.2 )i Bsin (28.2°)j The vector Cis given as :-27j The sum of the vectors A+B+C is zero if the x component of vector A is equal to the x component of vector B and the sum of the y component of vector A and B is equal to vector C. That is, The sum of the vectors A+ B + C is, А+ B+C-Acos(44.4° ): + Asin(44. 4° )j - B cos(28.2° )i + Bsin (28.2 )j-27, oi +oj-(4cos(444)- Bcos(28 Asin(44.4)+Bsin(28.2")-27)

Compare the x component in the above equation. A cos 44.4°-Bcos (28.2°)0 Acos(44.4)-Bcos (28.2 Bcos 28.2 cos44.4 1.2335B 0 Compare the y component in the above equation and determine the magnitude of vector B A sin44.4° + B sin (28.2)-27 0 (1.2335B)sin(44.4)+Bsin(28.2)-27 B(0.863+0.4725) 27 В 20.21 59 20.2 The magnitude of vector A is A= 1"2335B 1.2335(20.2159) 24.9