Fa vector has magnitude v_1 = 46 n, and direction theta_1 = 30 degree another vector v_2 = 63 n, and direction theta_2 = 151 degree. calculate the reference angle of the vector v_1 + v_2. round your answer such that it has no decimal.

105.8 degree from + X axis

Explanation:

V1 = 46 N at 30 degree

V2 = 63 N at 151 degree

Write the vector form

V1 = 46 (Cos 30 i + Sin 30 j) = 39.84 i + 23 j

V2 = 63 (Cos 151 i + Sin 151 j) = - 55 i + 30.54 j

The resultant of V1 and V2 is given by

V = V1 + V2 = 39.84 i + 23 j - 55 i + 30.54 j = - 15.16 i + 53.54 j

The angle made by resultant of V1 and V2 with X axis is

tan∅ = 53.54 / (- 15.16) = - 3.53

∅ = 105.8 degree from + X axis.

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