The magnitude of the sum of the two vectors is 20.22 m and the direction of the two vectors, A + B is 50⁰.
Magnitude of Sum of vector A+B
The magnitude of the sum of the two vectors is calculated as follows;
Bx = Bcosθ
By = Bsinθ
Bx = 15 m x cos(30) = 12.99 m
By = 15 x sin(30) = 7.5 m
Ax = 8 m x cos(90) = 0 m
Ay = 8 x sin(90) = 8 m
Ax + Bx = 0 + 12.99 m = 12.99 m
Ay + By = 8m + 7.5 m = 15.5 m
R = √12.99² + 15.5²
R = 20.22 m
Direction of the vectors
tanθ = 15.5/12.99
tanθ = 1.19
θ = 50⁰
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