3 Students and a Image of three vectors: A is along the +x axis, B is along the

Question

3 Students and a Image of three vectors: A is along the +x axis, B is along the +y axis and C is directed at an angle theta above the -x axis Three students converge on the last textbook in the store. All three grab it and begin to pull in the directions shown in the above figure. Student A exerts a force of 31.06 N, student B pulls with a force of 13.20 N, and student C pulls with a force of 44.35 N at an angle (theta)=76.87 degrees above the -x axis.

Considering these three forces (ignore the force of gravity on the book), what is the magnitude of the net force on the book? (Note: The figure is not drawn to scale.)

Give the angle of the resultant force with respect to the +x-axis. Assume the counter-clockwise direction to be positive and the clockwise direction to be negative.

Explanation / Answer

break into vector x, y components
A = 31.06i
B = 13.20 j
C = -44.35cos76.87 i + 44.35sin76.87 j
C = -10.07 i + 43.2j

R = A + B + C
R=20.99i + 56.39j N
|R| = (20.992 + 56.392)
|R| = 60.17 N
tan = 56.39 / 20.99
= 69.6o above the positive x axis

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