Two forces are applied to a tree stump to pull it out of the ground. force a has a magnitude of 2580 newtons (n) and points 36.0 ° south of east, while force b has a magnitude of 2270 n and points due south. using the component method, find the (a) magnitude and (b) direction of the resultant force a + b that is applied to the stump. specify the direction as a positive angle with respect to due east.

(a) 4323.67 N

(b) 421.13 degree

Explanation:

A = 2580 N 36 degree South of east

B = 2270 N due South

A = 2580 ( Cos 36 i - Sin 36 j) = 2087.26 i - 1516.49 j

B = 2270 (-j) = - 2270 j

A + B = 2087.26 i - 1516.49 j - 2270 j

A + B = 2087.26 i - 3786.49 j

(a) Magnitude of A + B =

Magnitude of A + B = 4323.67 N

(b) Direction of A + B

Tan theta = - 3786.49 / 2087.26

theta = - 61.13 degree

Angle from ast = 360 - 61.13 = 421.13 degree.

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