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Question

The figure shows two displacement vectors A and B. Vector A points at an angle of 18.0 degrees above the x-axis and has an unknown magnitude. Vector B has an x component B_x=36.0m and has an unknown y component B_y. These two vectors are equal. Find (a) the magnitude of A and (b) the value of B_y.

Answer 1

Because the two vectors are equal, we can superimpose them onto a single triangle with angle 18° and horizontal leg 36m. Then use trig: cos 18.0 = 36.0 / |A|, |A| = 36.0 /0.9511 = 37.9 m; tan 18.0 = B_y / 36.0, B_y = 11.7 m.