NOTE: In part 2 I think the rather cumbersome explanation means that the angle i

Question

NOTE: In part 2 I think the rather cumbersome explanation means that the angle is measured from the positive x-direction. if the y-component of the resultant vector is in the positive y-direction then the angle is positive. if the y-component of the resultant vector is in the negative y-direction then the angle is negative. Consider two vectors F~ 1 and F~ 2 with magnitude F1 = 71 N and F2 = 82 N and where 1 = 17 and 2 = 65 . 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 kF~ k, 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 angular direction, between the limits of 180 and +180 as measured from the positive x axis. Answer in units of .

Explanation / Answer

x-component of F1 is F1x = 71*cos(17) = 67.9 N

y-component of F1 is F1y = 71*sin(17) = 20.75 N

x-component of F2 is F2x = 82*cos(65) = 34.65 N

y-component of F2 is F2y = 82*sin(65) = 74.3 N

x-component of net force is F1x+F2x = 67.9+34.65 = 102.55 N

y-component of net force is F1y + F2y = 20.75 + 74.3 = 95.05 N

net force is Fnet = sqrt(102.55^2+95.05^2) = 139.82 N

direction theta = tan^(-1)(95.05/102.55) = 42.82 degrees

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