f a 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.