A vector F_1 vector has a magnitude of 40.0 units and points 35.0 degree above t

Question

A vector F_1 vector has a magnitude of 40.0 units and points 35.0 degree above the positive x axis. A second vector F_2 vector has a magnitude of 65.0 units and points in the negative x direction. Use the component method of vector addition to find the magnitude and direction, relative to the positive x axis, of the resultant F = F_1 vector + F_2 vector. 53.3 units, 141.8 degree relative to the + x axis 53.3 units, 52.1 degree units relative to the + x axis 39.6 units, 125.4 degree relative to the + x axis 39.6 units, 54.6 degree relative to the + x axis 46.2 units, 136.0 degree relative to the + x axis

Explanation / Answer

F1 = 40 cos 35 i + 40 sin 35 j

= 32.76 i + 22.94 j

F2 = -65 i

F = F1 + F2

= (32.76i + 22.94j) - 65i

= -32.24 i + 22.94 j

magnitude of F = sqrt(32.24^2 + 22.94^2) = 39.6

angle = 90 + tan^-1 ( 22.94 / 32.24) = 125.4 o relative to the x- axis

so option c) is the correct answer

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