The magnitude of the resultant vector is 22.6 m and the direction is 56.8⁰.
Resolution of vector A into x and y components
Ax = A cosθ
Ay = A sinθ
Ax = 7.7 x cos(27.8)
Ax = 6.81 m
Ay = 7.7 x sin(27.8)
Ay = 3.59 m
Resolution of vector B into x and y components
Bx = B cosθ
By = B sinθ
θ with respect to x - axis = 90 - 20 = 70⁰
Bx = 16.3 m x cos(70)
Bx = 5.575 m
By = 16.3 m x sin(70)
By = 15.32 m
Sum of vectors in x direction
Vx = Ax + Bx
Vx = 6.81 m + 5.575 m = 12.385 m
Sum of vectors in y direction
Vy = Ay + By
Vy = 3.59 m + 15.32 m = 18.91 m
Resultant vector
V = √(Vy² + Vx²)
V = √(18.91² + 12.385²)
V = 22.6 m
Direction of the vector
tan θ = Vy/Vx
tan θ = (18.91)/(12.385)
tan θ = 1.527
θ = arc tan (1.527)
θ = 56.8⁰
Thus, the magnitude of the resultant vector is 22.6 m and the direction is 56.8⁰.
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