Consider two vectors F_1 and F_2 with magnitude F_1 = 89 N and F_2 = 75 N and wh

Question

Consider two vectors F_1 and F_2 with magnitude F_1 = 89 N and F_2 = 75 N and where theta_1 = 33 degree and theta_2 = 175 degree. The angles are measured from the positive x axis with the counter-clockwise angular direction as positive. What is the magnitude of the resultant vector ||F||, where F = F_1 + F_2? Answer in units of N. What is the direction of this resultant vector F? Use counterclockwise as the positive se angular direction, between the limits of -180 degree and +180 degree as measured from the positive x axis. Answer in units of degree.

Explanation / Answer

F1x = 89*cos 33 deg

F1y = 89*sin 33 deg

F2x = -75*cos 5 deg

F2y = 75*sin 5 deg

Fx = 89*cos 33 deg - 75*cos 5 deg = -0.0729 N

Fy = 89*sin 33 deg + 75*sin 5 deg = 55.00 N

Fnet = sqrt (0.0729^2 + 55^2) = 55 N

B.

Direction = arctan (Fy/Fx)

= arctan (55/(-0.0729)) = 89.92 deg from - x axis

= 90.08 deg from +x-axis

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